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24 pages, 683 KiB  
Article
MtAD-Net: Multi-Threshold Adaptive Decision Net for Unsupervised Synthetic Aperture Radar Ship Instance Segmentation
by Junfan Xue, Junjun Yin and Jian Yang
Remote Sens. 2025, 17(4), 593; https://doi.org/10.3390/rs17040593 (registering DOI) - 9 Feb 2025
Abstract
In synthetic aperture radar (SAR) images, pixel-level Ground Truth (GT) is a scarce resource compared to Bounding Box (BBox) annotations. Therefore, exploring the use of unsupervised instance segmentation methods to convert BBox-level annotations into pixel-level GT holds great significance in the SAR field. [...] Read more.
In synthetic aperture radar (SAR) images, pixel-level Ground Truth (GT) is a scarce resource compared to Bounding Box (BBox) annotations. Therefore, exploring the use of unsupervised instance segmentation methods to convert BBox-level annotations into pixel-level GT holds great significance in the SAR field. However, previous unsupervised segmentation methods fail to perform well on SAR images due to the presence of speckle noise, low imaging accuracy, and gradual pixel transitions at the boundaries between targets and background, resulting in unclear edges. In this paper, we propose a Multi-threshold Adaptive Decision Network (MtAD-Net), which is capable of segmenting SAR ship images under unsupervised conditions and demonstrates good performance. Specifically, we design a Multiple CFAR Threshold-extraction Module (MCTM) to obtain a threshold vector by a false alarm rate vector. A Local U-shape Feature Extractor (LUFE) is designed to project each pixel of SAR images into a high-dimensional feature space, and a Global Vision Transformer Encoder (GVTE) is designed to obtain global features, and then, we use the global features to obtain a probability vector, which is the probability of each CFAR threshold. We further propose a PLC-Loss to adaptively reduce the feature distance of pixels of the same category and increase the feature distance of pixels of different categories. Moreover, we designed a label smoothing module to denoise the result of MtAD-Net. Experimental results on the dataset show that our MtAD-Net outperforms traditional and existing deep learning-based unsupervised segmentation methods in terms of pixel accuracy, kappa coefficient, mean intersection over union, frequency weighted intersection over union, and F1-Score. Full article
21 pages, 10628 KiB  
Article
Thermal Video Enhancement Mamba: A Novel Approach to Thermal Video Enhancement for Real-World Applications
by Sargis Hovhannisyan, Sos Agaian, Karen Panetta and Artyom Grigoryan
Information 2025, 16(2), 125; https://doi.org/10.3390/info16020125 (registering DOI) - 9 Feb 2025
Viewed by 127
Abstract
Object tracking in thermal video is challenging due to noise, blur, and low contrast. We present TVEMamba, a Mamba-based enhancement framework with near-linear complexity that improves tracking in these conditions. Our approach uses a State Space 2D (SS2D) module integrated with Convolutional Neural [...] Read more.
Object tracking in thermal video is challenging due to noise, blur, and low contrast. We present TVEMamba, a Mamba-based enhancement framework with near-linear complexity that improves tracking in these conditions. Our approach uses a State Space 2D (SS2D) module integrated with Convolutional Neural Networks (CNNs) to filter, sharpen, and highlight important details. Key components include (i) a denoising module to reduce background noise and enhance image clarity, (ii) an optical flow attention module to handle complex motion and reduce blur, and (iii) entropy-based labeling to create a fully labeled thermal dataset for training and evaluation. TVEMamba outperforms existing methods (DCRGC, RLBHE, IE-CGAN, BBCNN) across multiple datasets (BIRDSAI, FLIR, CAMEL, Autonomous Vehicles, Solar Panels) and achieves higher scores on standard quality metrics (EME, BDIM, DMTE, MDIMTE, LGTA). Extensive tests, including ablation studies and convergence analysis, confirm its robustness. Real-world examples, such as tracking humans, animals, and moving objects for self-driving vehicles and remote sensing, demonstrate the practical value of TVEMamba. Full article
(This article belongs to the Special Issue Emerging Research in Object Tracking and Image Segmentation)
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Figure 1
<p>(<b>a</b>,<b>c</b>) Challenging thermal video frames. (<b>b</b>,<b>d</b>) Successful recovery and enhancement by TVEMamba.</p>
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<p>(<b>a</b>) Overall architecture of TVEMamba, (<b>b</b>) Basic denoising state space model and attention-based state space model, and (<b>c</b>) Basic denoising module and optical flow attention module.</p>
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<p>This figure shows the original image from FLIR [<a href="#B40-information-16-00125" class="html-bibr">40</a>], the corresponding sharpened image, denoised images with different noise levels, and the final merged result.</p>
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<p>Visual comparison on (<b>a</b>) BIRDSAI [<a href="#B50-information-16-00125" class="html-bibr">50</a>], (<b>b</b>) FLIR [<a href="#B40-information-16-00125" class="html-bibr">40</a>], (<b>c</b>) CAMEL [<a href="#B51-information-16-00125" class="html-bibr">51</a>], and (<b>d</b>) Autonomous Vehicles [<a href="#B52-information-16-00125" class="html-bibr">52</a>] datasets.</p>
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<p>Performance of TVEMamba on BIRDSAI dataset.</p>
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<p>Qualitative results of TVEMamba framework on Solar Panel video frames.</p>
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<p>Evaluation of the contribution of OFA and BD Blocks in TVEMamba on the FLIR dataset.</p>
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<p>Details of intermediate results from the proposed TVEMamba, showing the effects of each module.</p>
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<p>Object detection results on original and enhanced Images using the YOLOR method.</p>
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26 pages, 1170 KiB  
Article
Preamble-Based Signal-to-Noise Ratio Estimation for Adaptive Modulation in Space–Time Block Coding-Assisted Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing System
by Shahid Manzoor, Noor Shamsiah Othman and Mohammed W. Muhieldeen
Algorithms 2025, 18(2), 97; https://doi.org/10.3390/a18020097 (registering DOI) - 9 Feb 2025
Viewed by 126
Abstract
This paper presents algorithms to estimate the signal-to-noise ratio (SNR) in the time domain and frequency domain that employ a modified Constant Amplitude Zero Autocorrelation (CAZAC) synchronization preamble, denoted as CAZAC-TD and CAZAC-FD SNR estimators, respectively. These SNR estimators are invoked in a [...] Read more.
This paper presents algorithms to estimate the signal-to-noise ratio (SNR) in the time domain and frequency domain that employ a modified Constant Amplitude Zero Autocorrelation (CAZAC) synchronization preamble, denoted as CAZAC-TD and CAZAC-FD SNR estimators, respectively. These SNR estimators are invoked in a space–time block coding (STBC)-assisted multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system. These SNR estimators are compared to the benchmark frequency domain preamble-based SNR estimator referred to as the Milan-FD SNR estimator when used in a non-adaptive 2×2 STBC-assisted MIMO-OFDM system. The performance of the CAZAC-TD and CAZAC-FD SNR estimators is further investigated in the non-adaptive 4×4 STBC-assisted MIMO-OFDM system, which shows improved bit error rate (BER) and normalized mean square error (NMSE) performance. It is evident that the non-adaptive 2×2 and 4×4 STBC-assisted MIMO-OFDM systems that invoke the CAZAC-TD SNR estimator exhibit superior performance and approach closer to the normalized Cramer–Rao bound (NCRB). Subsequently, the CAZAC-TD SNR estimator is invoked in an adaptive modulation scheme for a 2×2 STBC-assisted MIMO-OFDM system employing M-PSK, denoted as the AM-CAZAC-TD-MIMO system. The AM-CAZAC-TD-MIMO system outperformed the non-adaptive STBC-assisted MIMO-OFDM system using 8-PSK by about 2 dB at BER = 104. Moreover, the AM-CAZAC-TD-MIMO system demonstrated an SNR gain of about 4 dB when compared with an adaptive single-input single-output (SISO)-OFDM system with M-PSK. Therefore, it was shown that the spatial diversity of the MIMO-OFDM system is key for the AM-CAZAC-TD-MIMO system’s improved performance. Full article
21 pages, 2900 KiB  
Article
Robust Beamforming for Frequency Diverse Array Multiple-Input Multiple-Output Radar: Mitigating Steering Vector Mismatches and Suppressing Main Lobe Interference
by Yumei Tan, Yong Li, Wei Cheng, Limeng Dong, Langhuan Geng and Muhammad Moin Akhtar
Remote Sens. 2025, 17(4), 577; https://doi.org/10.3390/rs17040577 (registering DOI) - 8 Feb 2025
Viewed by 130
Abstract
Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar introduces range-dependent beamforming capabilities, enhancing its ability to differentiate true targets from main lobe jammers. However, this innovation also introduces new challenges, particularly when errors disrupt the transceiver steering vectors, leading to performance degradation in main [...] Read more.
Frequency Diverse Array Multiple-Input Multiple-Output (FDA-MIMO) radar introduces range-dependent beamforming capabilities, enhancing its ability to differentiate true targets from main lobe jammers. However, this innovation also introduces new challenges, particularly when errors disrupt the transceiver steering vectors, leading to performance degradation in main lobe interference suppression. To this end, a robust beamforming method tailored for FDA-MIMO radar systems is proposed to address signal mismatches caused by range–angle errors, array element position errors, frequency offsets, and coherent local scattering. Initially, a logarithmic function is used to decouple range and angle, enabling the design of a stable beampattern. The desired steering vector is then computed by addressing an optimization problem that leverages the interference-plus-noise covariance matrix alongside the signal-plus-noise covariance matrix. This estimation process, combined with mismatch correction through the diagonal loading method, significantly stabilizes the covariance matrix and enhances the robustness of FDA-MIMO systems. Extensive simulations validate the proposed approach across various error scenarios specific to FDA-MIMO radars, demonstrating superior robustness in main lobe interference suppression. These findings contribute to advancing robust beamforming techniques for FDA-MIMO radar systems, paving the way for enhanced performance in complex and error-prone environments. Full article
20 pages, 4545 KiB  
Article
Comparative Analysis of Fractals-Homogeneity-Entropy Algorithms Applied on a FEM Bridge Model to Identify Damage
by Jose M. Machorro-Lopez, Martin Valtierra-Rodriguez, Jose T. Perez-Quiroz and Juan P. Amezquita-Sanchez
Infrastructures 2025, 10(2), 36; https://doi.org/10.3390/infrastructures10020036 (registering DOI) - 8 Feb 2025
Viewed by 183
Abstract
Vehicular bridges accumulate damage over time due to overloads and material degradation. Non-visible structural damage in such large structures poses a serious risk, as small defects in critical elements can rapidly grow, potentially leading to catastrophic failure. Therefore, implementing simple yet effective methods [...] Read more.
Vehicular bridges accumulate damage over time due to overloads and material degradation. Non-visible structural damage in such large structures poses a serious risk, as small defects in critical elements can rapidly grow, potentially leading to catastrophic failure. Therefore, implementing simple yet effective methods for damage identification within a structural health monitoring (SHM) system is crucial for ensuring bridge reliability. This study presents a systematic comparative analysis of multiple damage detection algorithms, including six different fractal dimensions (FDs), the homogeneity index (HI), and the Shannon entropy index (SEI). These methods are applied to a high-fidelity finite element method (FEM) model of the Rio Papaloapan Bridge (RPB), a cable-stayed structure, to detect and localize two different types of damage (deck and cable failures) with varying severities and positions. To enhance practical applicability, realistic conditions are simulated by introducing noise to the vibration signals collected from both the undamaged and damaged bridge scenarios while a moving load, simulating a vehicle, is crossing. The results indicate that the HI and SEI not only detected and localized all damage scenarios but also effectively distinguished between different levels of severity, making them highly promising for SHM applications. Additionally, two of the six FD algorithms successfully identified all damage cases with minimal variation from the healthy condition, demonstrating their potential utility. The findings presented in this study are consistent with previous experimental and real-world bridge assessments, reinforcing their validity for real-life applications. Full article
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<p>Picture of the RPB.</p>
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<p>Schematic sketch of the RPB.</p>
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<p>FEM model of the RPB in ANSYS©.</p>
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<p>Schematic diagram of the proposed methodology.</p>
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<p>Structural conditions: (<b>a</b>) healthy, (<b>b</b>) incipient damage on deck, (<b>c</b>) moderate damage on deck, (<b>d</b>) severe damage on deck, and (<b>e</b>) moderate damage on cable.</p>
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<p>Waveform plot for filtered signals of condition 1 and condition 2 registered at 0.75 L.</p>
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<p>Absolute average (S1–S3) variation percentage with respect to the healthy condition for (<b>a</b>) all the DI and (<b>b</b>) only the FD.</p>
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17 pages, 4941 KiB  
Article
Underwater Target Localization Method Based on Uniform Linear Electrode Array
by Wenjing Shang, Feixiang Gao, Jiahui Liu, Yunhe Pang, Sergey V. Volvenko, Vladimir M. Olshanskiy and Yidong Xu
J. Mar. Sci. Eng. 2025, 13(2), 306; https://doi.org/10.3390/jmse13020306 - 6 Feb 2025
Viewed by 423
Abstract
The underwater electric field signal can be excited by underwater vehicles, such as the shaft-rate electric field and the corrosion electric field. The electric field signature of each vehicle exhibits significant differences in time and frequency domain, which can be exploited to determine [...] Read more.
The underwater electric field signal can be excited by underwater vehicles, such as the shaft-rate electric field and the corrosion electric field. The electric field signature of each vehicle exhibits significant differences in time and frequency domain, which can be exploited to determine target positions. In this paper, a novel passive localization method for underwater targets is presented, leveraging a uniform linear electrode array (ULEA). The ULEA manifold along the axial direction is derived from the electric field propagation in an infinite lossy medium, which provides the nonlinear mapping relationship between the target position and the voltage data acquired by the ULEA. In order to locate the targets, the multiple signal classification (MUSIC) algorithm is applied. Then, capitalizing on the rotational invariance of matrix operations and exploiting the symmetry inherent in the ULEA, we streamline the six-dimensional spatial spectral scanning onto a two-dimensional plane, providing azimuth and distance information for the targets. This method significantly reduces computational overhead. To validate the efficacy of our proposed method, we devise a localization system and conduct a simulation environment to estimate targets. Results show that our method achieves satisfactory direction and reliable distance estimations, even in scenarios with low signal-to-noise ratios. Full article
(This article belongs to the Special Issue Intelligent Measurement and Control System of Marine Robots)
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<p>ULEA vector rotate model, where the vectors <math display="inline"><semantics> <msub> <mi mathvariant="bold">e</mi> <mi>p</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold">e</mi> <msub> <mi>r</mi> <mi>k</mi> </msub> </msub> </semantics></math> are rotated <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math> along the <span class="html-italic">x</span>-axis.</p>
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<p>ULEA vector rotate model, where the vectors <math display="inline"><semantics> <msub> <mi mathvariant="bold">e</mi> <mi>p</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi mathvariant="bold">e</mi> <msub> <mi>r</mi> <mi>k</mi> </msub> </msub> </semantics></math> are rotated <math display="inline"><semantics> <mi>θ</mi> </semantics></math> along the <span class="html-italic">x</span>-axis.</p>
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<p>The synthetic electric field of two electric sources.</p>
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<p>The spatial spectrum in range <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>∈</mo> <mo>(</mo> <msup> <mn>20</mn> <mo>∘</mo> </msup> <mo>,</mo> <mo> </mo> <msup> <mn>160</mn> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>∈</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>,</mo> <mo> </mo> <mn>100</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>a</b>) SNR = 20 dB. (<b>b</b>) SNR = 10 dB. (<b>c</b>) SNR = 6 dB. (<b>d</b>) The spatial spectrum slice when <math display="inline"><semantics> <msub> <mi>r</mi> <mn>0</mn> </msub> </semantics></math> = 73 m. (<b>e</b>) The spatial spectrum slice when <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>The azimuth precision with various SNR.</p>
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<p>The spatial spectrum of two electric sources at parameter points <math display="inline"><semantics> <mrow> <mo stretchy="false">(</mo> <msup> <mn>80</mn> <mo>∘</mo> </msup> <mo>±</mo> <mstyle scriptlevel="0" displaystyle="false"> <mfrac> <mrow> <mo>Δ</mo> <mi>φ</mi> </mrow> <mn>2</mn> </mfrac> </mstyle> <mo>,</mo> <mo> </mo> <mn>70</mn> <mo> </mo> <mi mathvariant="normal">m</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> under the condition SNR <math display="inline"><semantics> <mrow> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> dB.</p>
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<p>The spatial spectrum of two electric sources at parameter points <math display="inline"><semantics> <mrow> <mo>(</mo> <msup> <mn>90</mn> <mo>∘</mo> </msup> <mo>,</mo> <mo> </mo> <mn>40</mn> <mo>±</mo> <mstyle scriptlevel="0" displaystyle="false"> <mfrac> <mrow> <mo>Δ</mo> <mi>r</mi> </mrow> <mn>2</mn> </mfrac> </mstyle> <mo>)</mo> </mrow> </semantics></math> under the condition SNR <math display="inline"><semantics> <mrow> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math> dB.</p>
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<p>The azimuth precision with various ULEA element number <span class="html-italic">M</span> when the SNR is 20 dB.</p>
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<p>The azimuth estimation’s RMSE with various ULEA voltage sensor number <span class="html-italic">M</span>.</p>
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<p>The azimuth precision with various ULEA voltage sensor element interval <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>l</mi> </mrow> </semantics></math>.</p>
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<p>The spatial spectrum in range <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>∈</mo> <mo>(</mo> <msup> <mn>80</mn> <mo>∘</mo> </msup> <mo>,</mo> <mo> </mo> <msup> <mn>100</mn> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) The simulation settings <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, the azimuth difference is <math display="inline"><semantics> <msup> <mn>6</mn> <mo>∘</mo> </msup> </semantics></math>. (<b>b</b>) The simulation settings <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>l</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, the azimuth difference of the two electric sources is <math display="inline"><semantics> <msup> <mn>8</mn> <mo>∘</mo> </msup> </semantics></math>. (<b>c</b>) The simulation settings <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>l</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, the azimuth difference is <math display="inline"><semantics> <msup> <mn>2</mn> <mo>∘</mo> </msup> </semantics></math>. (<b>d</b>) The simulation settings <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>l</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math>, the azimuth difference is <math display="inline"><semantics> <msup> <mn>4</mn> <mo>∘</mo> </msup> </semantics></math>. (<b>e</b>) The simulation settings <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>l</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, the azimuth difference is <math display="inline"><semantics> <msup> <mn>2</mn> <mo>∘</mo> </msup> </semantics></math>. (<b>f</b>) The simulation settings <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>l</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, the azimuth difference is <math display="inline"><semantics> <msup> <mn>4</mn> <mo>∘</mo> </msup> </semantics></math>.</p>
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<p>The azimuth estimation’s RMSE with various ULEA element interval <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>l</mi> </mrow> </semantics></math> when the SNR is 20 dB.</p>
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15 pages, 5175 KiB  
Article
Research on Rapid and Non-Destructive Detection of Coffee Powder Adulteration Based on Portable Near-Infrared Spectroscopy Technology
by Fujie Zhang, Xiaoning Yu, Lixia Li, Wanxia Song, Defeng Dong, Xiaoxian Yue, Shenao Chen and Qingyu Zeng
Foods 2025, 14(3), 536; https://doi.org/10.3390/foods14030536 - 6 Feb 2025
Viewed by 258
Abstract
This study explores the feasibility of using portable near-infrared spectroscopy for the rapid and non-destructive detection of coffee adulteration. Spectral data from adulterated coffee samples in the 900–1700 nm range were collected and processed using five preprocessing methods. For qualitative detection, the Support [...] Read more.
This study explores the feasibility of using portable near-infrared spectroscopy for the rapid and non-destructive detection of coffee adulteration. Spectral data from adulterated coffee samples in the 900–1700 nm range were collected and processed using five preprocessing methods. For qualitative detection, the Support Vector Machine (SVM) algorithm was applied. For quantitative detection, two optimization algorithms, Invasive Weed Optimization (IWO) and Binary Chimp Optimization Algorithm (BChOA), were used for the feature wavelength selection. The results showed that convolution smoothing combined with multiple scattering correction effectively improved the signal-to-noise ratio. SVM achieved 96.88% accuracy for qualitative detection. For the quantitative analysis, the IWO algorithm identified key wavelengths, reducing data dimensionality by 82.46% and improving accuracy by 10.96%, reaching 92.25% accuracy. In conclusion, portable near-infrared spectroscopy technology can be used for the rapid and non-destructive qualitative and quantitative detection of coffee adulteration and can serve as a foundation for the further development of rapid, non-destructive testing devices. At the same time, this method has broad application potential and can be extended to various food products such as dairy, juice, grains, and meat for quality control, traceability, and adulteration detection. Through the feature wavelength selection method, it can effectively identify and extract spectral features associated with these food components (such as fat, protein, or characteristic compounds), thereby improving the accuracy and efficiency of detection, further ensuring food safety and enhancing the level of food quality control. Full article
(This article belongs to the Section Food Engineering and Technology)
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<p>Average Spectral Curves of Soybean (blue solid line), Barley (red solid line), Chicory (yellow solid line), Coffee (purple solid line), and Corn (green solid line).</p>
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<p>(<b>a</b>) Original; (<b>b</b>) SG preprocessing; (<b>c</b>) MSC preprocessing; (<b>d</b>) SG-MSC preprocessing; (<b>e</b>) SNV preprocessing; (<b>f</b>) SG-SNV preprocessing.</p>
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<p>SG-MSC-SVM Classification Results for Coffee Adulteration Detection.</p>
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<p>IWO feature extraction process (<b>left</b>) and results (<b>right</b>).</p>
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<p>BChOA feature extraction process (<b>left</b>) and results (<b>right</b>).</p>
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<p>IWO-SVM Quantitative Classification Results for Coffee Adulteration Detection.</p>
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26 pages, 4698 KiB  
Article
Estimating Motion Parameters of Ground Moving Targets from Dual-Channel SAR Systems
by Kun Liu, Xiongpeng He, Guisheng Liao, Shengqi Zhu and Cao Zeng
Remote Sens. 2025, 17(3), 555; https://doi.org/10.3390/rs17030555 - 6 Feb 2025
Viewed by 316
Abstract
In dual-channel synthetic aperture radar (SAR) systems, the estimation of the four-dimensional motion parameters of the ground maneuvering target is a critical challenge. In particular, when spatial degrees of freedom are used to enhance the target’s output signal-to-clutter-plus-noise ratio (SCNR), it is possible [...] Read more.
In dual-channel synthetic aperture radar (SAR) systems, the estimation of the four-dimensional motion parameters of the ground maneuvering target is a critical challenge. In particular, when spatial degrees of freedom are used to enhance the target’s output signal-to-clutter-plus-noise ratio (SCNR), it is possible to have multiple solutions in the parameter estimation of the target. To deal with this issue, a novel algorithm for estimating the motion parameters of ground moving targets in dual-channel SAR systems is proposed in this paper. First, the random sample consensus (RANSAC) and modified adaptive 2D calibration (MA2DC) are used to prevent the target’s phase from being distorted as a result of channel balancing. To address range migration, the RFRT algorithm is introduced to achieve arbitrary-order range migration correction for moving targets, and the generalized scaled Fourier transform (GSCFT) algorithm is applied to estimate the polynomial coefficients of the target. Subsequently, we propose using the synthetic aperture length (SAL) of the target as an independent equation to solve for the four-dimensional parameter information and introduce a windowed maximum SNR method to estimate the SAL. Finally, a closed-form solution for the four-dimensional parameters of ground maneuvering targets is derived. Simulations and real data validate the effectiveness of the proposed algorithm. Full article
(This article belongs to the Special Issue Advanced Techniques of Spaceborne Surveillance Radar)
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<p>Geometry relationship between a ground moving target and the SAR platform.</p>
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<p>The phase fitting results after the fifth iteration. (<b>a</b>) MA2DC. (<b>b</b>) MA2DC+RANSAC.</p>
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<p>Comparing the signal-to-noise Ratio (SNR) after applying RFRT using bandwidth and sampling frequency, respectively.</p>
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<p>The relationship between the search window length and the target’s SAL.</p>
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<p>Multiple target processing results. (<b>a</b>) The trajectory of targets. (<b>b</b>) The results of FFT along fast time. (<b>c</b>) RCMC by RFRT. (<b>d</b>) Cross interference of RFRT. (<b>e</b>) The results of GSCFT.</p>
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<p>The SAL estimation results and imaging results for Tar1. (<b>a</b>) Start time search result. (<b>b</b>) End time search result. (<b>c</b>) Ambiguity velocity search result. (<b>d</b>) Focusing result of Tar1.</p>
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<p>The SAL estimation results and imaging results for Tar2. (<b>a</b>) Start time search result. (<b>b</b>) End time search result. (<b>c</b>) Ambiguity velocity search result. (<b>d</b>) Focusing result of Tar2.</p>
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<p>The estimation performance of motion parameter. (<b>a</b>) Cross-track velocity. (<b>b</b>) Cross-track acceleration. (<b>c</b>) Along-track velocity. (<b>d</b>) Along-track acceleration.</p>
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<p>The interference phase results after processing by different channel balancing algorithms. (<b>a</b>) MA2DC. (<b>b</b>) RANSAC+MA2DC.</p>
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<p>Parameter estimation results of the proposed algorithm in a dual-channel airborne SAR system. (<b>a</b>) Two-dimensional time domain result before clutter suppression. (<b>b</b>) Target motion trajectory after clutter rejection. (<b>c</b>) RCMC result by RFRT. (<b>d</b>) GSCFT result. (<b>e</b>) RCMC results after the compensation function. (<b>f</b>) Final focusing result by the proposed method. (<b>g</b>) Moving target relocation result after proposed method. (<b>h</b>) Moving target relocation result after MA2DC. (The red diamond represents the detection result of the moving target, and the green circle represents the relocation result of the moving target).</p>
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<p>Focusing results of different algorithms with Ku-band.</p>
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<p>SAL results of ground moving target. (<b>a</b>) Start time search result. (<b>b</b>) Start time search local result. (<b>c</b>) End time search result. (<b>d</b>) End time search local result.</p>
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<p>Parameter estimation results results for two ground moving targets in a real airborne SAR system. (<b>a</b>) Range–Doppler domain results before clutter suppression. (<b>b</b>) Range–Doppler domain result after clutter suppression. (<b>c</b>) RCMC result of target1 by RFRT. (<b>d</b>) RCMC result of target 2 by RFRT. (<b>e</b>) GSCFT result of target 1 (<b>f</b>) GSCFT result of target 2. (<b>g</b>) The result of compensating of target 1 after Equation (<a href="#FD30-remotesensing-17-00555" class="html-disp-formula">30</a>). (<b>h</b>) The result of compensating of target 2 after Equation (<a href="#FD30-remotesensing-17-00555" class="html-disp-formula">30</a>). (<b>i</b>) Final focusing result of target 1 by the proposed method. (<b>j</b>) Final focusing result of target 2 by the proposed method. (<b>k</b>) Ambiguity search result of target’s radial velocity. (<b>l</b>) Relocation result of targets. (The red diamond represents the detection result of the moving target, and the green circle represents the relocation result of the moving target).</p>
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<p>Parameter estimation results results for two ground moving targets in a real airborne SAR system. (<b>a</b>) Range–Doppler domain results before clutter suppression. (<b>b</b>) Range–Doppler domain result after clutter suppression. (<b>c</b>) RCMC result of target1 by RFRT. (<b>d</b>) RCMC result of target 2 by RFRT. (<b>e</b>) GSCFT result of target 1 (<b>f</b>) GSCFT result of target 2. (<b>g</b>) The result of compensating of target 1 after Equation (<a href="#FD30-remotesensing-17-00555" class="html-disp-formula">30</a>). (<b>h</b>) The result of compensating of target 2 after Equation (<a href="#FD30-remotesensing-17-00555" class="html-disp-formula">30</a>). (<b>i</b>) Final focusing result of target 1 by the proposed method. (<b>j</b>) Final focusing result of target 2 by the proposed method. (<b>k</b>) Ambiguity search result of target’s radial velocity. (<b>l</b>) Relocation result of targets. (The red diamond represents the detection result of the moving target, and the green circle represents the relocation result of the moving target).</p>
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<p>Focusing results of different algorithms with X-band. (<b>a</b>) Target 1. (<b>b</b>) Target 2.</p>
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18 pages, 3840 KiB  
Article
An Enhanced Contrastive Ensemble Learning Method for Anomaly Sound Detection
by Jingneng Liao, Fei Yang and Xiaoqing Lu
Appl. Sci. 2025, 15(3), 1624; https://doi.org/10.3390/app15031624 (registering DOI) - 5 Feb 2025
Viewed by 703
Abstract
This paper proposes an enhanced contrastive ensemble learning method for anomaly sound detection. The proposed method achieves approximately 6% in the AUC metric in some categories and achieves state-of-the-art performance among self-supervised models on multiple benchmark datasets. The proposed method is effective in [...] Read more.
This paper proposes an enhanced contrastive ensemble learning method for anomaly sound detection. The proposed method achieves approximately 6% in the AUC metric in some categories and achieves state-of-the-art performance among self-supervised models on multiple benchmark datasets. The proposed method is effective in automatically monitoring the operating conditions of the production equipment by detecting the sounds emitted by the machine, to provide an early warning of potential production accidents. This method can significantly reduce industrial monitoring costs and increase monitoring efficiency to improve manufacturing facility productivity effectively. Existing detection methods face challenges with data imbalance caused by the scarcity of anomalous samples, leading to performance degradation. This paper proposes an enhanced data augmentation method that improves model robustness by allowing the data to retain the original features while adding noise close to the real environment through a simple operation. Secondly, model feature extraction is enhanced by using channel attention to fuse time-frequency features. Thirdly, this paper proposes a simple anomaly sample generation method, which can automatically generate real pseudo anomaly samples to help the model gain anomaly detection capability and reduce the impact of data imbalance. Finally, this paper proposes a statistical-based bias compensation that further mitigates the impact of data imbalance by distributing samples through statistical induction. Experimental verification confirms that these changes enhance anomalous sound detection capability. Full article
(This article belongs to the Special Issue Artificial Intelligence in Fault Diagnosis and Signal Processing)
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<p>Spec1 and Spec2 represent two different spectrograms, and the cropping points for each axis in each spectrogram are complementary.</p>
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<p>Model structure: The model is divided in two sections, the upper section is the pre-trained model and the lower is the fine-tuned model.</p>
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<p>Negative examples: SF denotes spectrogram flip, SP denotes spectrogram plus. The color represents the energy at each sampling point, with brighter colors indicating higher energy levels.</p>
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<p>Block structure: This block contains three convolutional sub-blocks which together form an inverted residual module. In each inverted residual module, there is a dimension-increasing layer with a 1 × 1 convolution, a feature extraction layer with a 3 × 3 convolution and a dimension-decreasing layer with a 1 × 1 convolution. After each convolutional kernel, batchnorm and leakyrelu activation functions are employed. When stride is set to one, the block uses shortcut connection.</p>
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<p>Time-Spec domain fusion model: <span class="html-italic">w</span> and <span class="html-italic">h</span> represent the shape of feature map, <span class="html-italic">c</span> represents the number of channels. During Squeeze-Excitation, the model first squeezes the feature map along the channel dimension, then derives weights for each channel and finally applies these weights to the corresponding channels of the original map.</p>
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<p>Global weight average pooling process.</p>
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<p>FAR-FRR curve within the MIMII datset.</p>
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17 pages, 2573 KiB  
Article
Rectifier Fault Diagnosis Based on Euclidean Norm Fusion Multi-Frequency Bands and Multi-Scale Permutation Entropy
by Jinping Liang and Xiangde Mao
Electronics 2025, 14(3), 612; https://doi.org/10.3390/electronics14030612 - 5 Feb 2025
Viewed by 334
Abstract
With the emphasis on energy conversion and energy-saving technologies, the single-phase pulse width modulation (PWM) rectifier method is widely used in urban rail transit because of its advantages of bidirectional electric energy conversion and higher power factor. However, due to the complex control [...] Read more.
With the emphasis on energy conversion and energy-saving technologies, the single-phase pulse width modulation (PWM) rectifier method is widely used in urban rail transit because of its advantages of bidirectional electric energy conversion and higher power factor. However, due to the complex control and harsh environment, it can easily fail. Faults can cause current and voltage distortion, harmonic increases and other problems, which can threaten the safety of the power system and the train. In order to ensure the stable operation of the rectifier, incidences of faults should be reduced. A fault diagnosis technique based on Euclidean norm fusion multi-frequency bands and multi-scale permutation entropy is proposed. Firstly, by the optimal wavelet function, information on the optimal multi-frequency bands of the fault signal is selected after wavelet packet decomposition. Secondly, the multi-scale permutation entropy of each frequency band is calculated, and multiple fault feature vectors are obtained for each frequency band. To reduce the classifier’s computational cost, the Euclidean norm is used to fuse the multi-scale permutation entropy into an entropy value, so that each frequency band uses an entropy value to characterize the fault information features. Finally, the optimal multi-frequency bands and multi-scale permutation entropy after fusion are used as the fault feature vector. In the simulation system, it is shown that the method’s average accuracy is 78.46%, 97.07%, and 99.45% when the SNR is 5 dB, 10 dB, and 15 dB, respectively. And the fusion of multi-scale permutation entropy can improve the accuracy, recall rate, precision, and F1 score and reduce the False Alarm Rate (FAR) and the Missing Alarm Rate (MAR). The results show that the fault diagnosis method has high diagnosis accuracy, is a simple feature fusion method, and has good robustness to working conditions and noise. Full article
(This article belongs to the Section Power Electronics)
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<p>Main components in the traction transmission system and their failure rates.</p>
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<p>A single-phase PWM rectifier circuit structure.</p>
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<p>T1 OC fault.</p>
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<p>T1 and T3 OC faults.</p>
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<p>D1 OC fault.</p>
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<p>Fault diagnosis block diagram.</p>
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<p>The input voltage waveform under different output voltages. (<b>a</b>) <span class="html-italic">U</span><sub>out</sub> = 2800 V. (<b>b</b>) <span class="html-italic">U</span><sub>out</sub> = 2600 V.</p>
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<p>Fault diagnosis results of optimal multi-frequency band permutation entropy.</p>
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<p>SVM diagnosis results of fuzzy entropy feature fusion at different scales.</p>
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25 pages, 43021 KiB  
Article
Interlayer Parallel Connection of Multiple Helmholtz Resonators for Optional Broadband Low Frequency Sound Absorption
by Xiaocui Yang, Qiang Li, Xinmin Shen, Binbin Zhou, Ning Wang, Enshuai Wang, Xiaonan Zhang, Cheng Shen, Hantian Wang and Shunjie Jiang
Materials 2025, 18(3), 682; https://doi.org/10.3390/ma18030682 - 4 Feb 2025
Viewed by 428
Abstract
The Helmholtz resonance acoustic metamaterial is an effective sound absorber in the field of noise reduction, especially in the low-frequency domain. To overcome the conflict between the number of Helmholtz resonators and the volume of the rear cavity for each chamber with a [...] Read more.
The Helmholtz resonance acoustic metamaterial is an effective sound absorber in the field of noise reduction, especially in the low-frequency domain. To overcome the conflict between the number of Helmholtz resonators and the volume of the rear cavity for each chamber with a given front area of single-layer metamaterial, a novel acoustic metamaterial of interlayer parallel connection of multiple Helmholtz resonators (IPC–MHR) is proposed in this study. The developed IPC–MHR consists of several layers, and the Helmholtz resonators among different layers are connected in parallel. The sound absorption property of IPC–MHR is studied by finite element simulation and further optimized by particle swarm optimization algorithm, and it is validated by standing wave tube measurement with the sample fabricated by additive manufacturing. The average sound absorption coefficient in the discrete frequency band [200 Hz, 300 Hz] U [400 Hz, 600 Hz] U [800 Hz, 1250 Hz] is 0.7769 for the IPC–MHR with four layers. Through the optimization of the thickness of each layer, the average sound absorption coefficient in 250–750 Hz is up to 0.8068. Similarly, the optimized IPC–MHR with six layers obtains an average sound absorption coefficient of 0.8454 in 300–950 Hz, which exhibits an excellent sound absorption performance in the low-frequency range with a wide band. The IPC–MHR can be used to suppress obnoxious noise in practical applications. Full article
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<p>The overall structure of the proposed IPC–MHR acoustic metamaterial.</p>
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<p>The structure of each layer in the IPC–MHR acoustic metamaterial. (<b>a</b>) The first layer; (<b>b</b>) the second layer; (<b>c</b>) the third layer; and (<b>d</b>) the fourth layer.</p>
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<p>The air domain of the proposed IPC–MHR acoustic metamaterial.</p>
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<p>The air domain of each layer in the IPC–MHR acoustic metamaterial. (<b>a</b>) The first layer; (<b>b</b>) the second layer; (<b>c</b>) the third layer; and (<b>d</b>) the fourth layer.</p>
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<p>The acoustic finite element simulation of the proposed IPC–MHR acoustic metamaterial. (<b>a</b>) The single-group IPC–MHR; and (<b>b</b>) the multi-group IPC–MHR.</p>
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<p>The distributions of sound absorption coefficients for the single-group IPC–MHR with the various side lengths of the square incident aperture: (<b>a</b>) 3 mm; (<b>b</b>) 4 mm; (<b>c</b>) 5 mm; (<b>d</b>) 6 mm; (<b>e</b>) 7 mm; (<b>f</b>) 8 mm; (<b>g</b>) 9 mm; and (<b>h</b>) 10 mm.</p>
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<p>The distributions of sound absorption coefficients for the single-group IPC–MHR with the various side lengths of the square incident aperture: (<b>a</b>) 3 mm; (<b>b</b>) 4 mm; (<b>c</b>) 5 mm; (<b>d</b>) 6 mm; (<b>e</b>) 7 mm; (<b>f</b>) 8 mm; (<b>g</b>) 9 mm; and (<b>h</b>) 10 mm.</p>
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<p>The distributions of the viscous power densities at the four resonance frequencies when the side length of the square incident aperture for the single-group IPC–MHR is 7 mm: (<b>a</b>) 231 Hz; (<b>b</b>) 470 Hz; (<b>c</b>) 887 Hz; and (<b>d</b>) 1147 Hz.</p>
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<p>The distributions of sound absorption coefficients for the multi-group IPC–MHR with the various combinations of side length of the square incident aperture for the 4 modules: (<b>a</b>) 6 mm + 7 mm + 8 mm + 9 mm; and (<b>b</b>) 6 mm +6.5 mm + 7 mm + 7.5 mm.</p>
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<p>The distributions of viscous power densities at 15 frequency points for the multi-group IPC–MHR when the side length of the square incident aperture for the 4 modules are 6 mm, 7 mm, 8 mm, and 9 mm: (<b>a</b>) 200 Hz; (<b>b</b>) 232 Hz; (<b>c</b>) 263 Hz; (<b>d</b>) 292 Hz; (<b>e</b>) 408 Hz; (<b>f</b>) 471 Hz; (<b>g</b>) 532 Hz; (<b>h</b>) 589 Hz; (<b>i</b>) 788 Hz; (<b>j</b>) 890 Hz; (<b>k</b>) 976 Hz; (<b>l</b>) 1073 Hz; (<b>m</b>) 1147 Hz; (<b>n</b>) 1192 Hz; and (<b>o</b>) 1250 Hz.</p>
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<p>The distributions of viscous power densities at 15 frequency points for the multi-group IPC–MHR when the side length of the square incident aperture for the 4 modules are 6 mm, 7 mm, 8 mm, and 9 mm: (<b>a</b>) 200 Hz; (<b>b</b>) 232 Hz; (<b>c</b>) 263 Hz; (<b>d</b>) 292 Hz; (<b>e</b>) 408 Hz; (<b>f</b>) 471 Hz; (<b>g</b>) 532 Hz; (<b>h</b>) 589 Hz; (<b>i</b>) 788 Hz; (<b>j</b>) 890 Hz; (<b>k</b>) 976 Hz; (<b>l</b>) 1073 Hz; (<b>m</b>) 1147 Hz; (<b>n</b>) 1192 Hz; and (<b>o</b>) 1250 Hz.</p>
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<p>The fabrication of the multi-group IPC–MHR when the side length of the square incident aperture for the 4 modules are 6 mm, 7 mm, 8 mm, and 9 mm. (<b>a</b>) The utilized additive manufacturing machine; (<b>b</b>) the first layer; (<b>c</b>) the second layer; (<b>d</b>) the third layer; (<b>e</b>) the fourth layer; and (<b>f</b>) the assembled multi-group IPC–MHR sample.</p>
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<p>The experimental validation of sound absorption performance of the multi-group IPC–MHR. (<b>a</b>) The utilized standing wave tube system; and (<b>b</b>) the comparisons of the sound absorption coefficients between simulation result and experimental data.</p>
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<p>The flow chart of the particle swarm optimization algorithm utilized in this research and the corresponding selected parameters.</p>
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<p>The distribution of optimal sound absorption property for the expected combinations of frequency domains 200–300 Hz, 400–600 Hz, and 800–1250 Hz.</p>
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<p>The finite element simulation of IPC–MHR acoustic metamaterial for the expected frequency range 250–750 Hz. (<b>a</b>) The single-group IPC–MHR; and (<b>b</b>) the multi-group IPC–MHR.</p>
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<p>The distribution of optimal sound absorption property for the expected frequency range of 250–750 Hz. (<b>a</b>) The overall sound absorption performance; (<b>b</b>) the first module; (<b>c</b>) the second module; (<b>d</b>) the third module; and (<b>e</b>) the fourth module.</p>
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<p>The finite element simulation of IPC–MHR acoustic metamaterial with 6 layers. (<b>a</b>) The single-group IPC–MHR; and (<b>b</b>) the multi-group IPC–MHR.</p>
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<p>The distribution of optimal sound absorption property for the expected frequency range of 300–950 Hz. (<b>a</b>) The overall sound absorption performance; (<b>b</b>) the first module; (<b>c</b>) the second module; (<b>d</b>) the third module; and (<b>e</b>) the fourth module.</p>
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<p>The distributions of the viscous power densities at the 20 marked frequency points in <a href="#materials-18-00682-f017" class="html-fig">Figure 17</a>a: (<b>a</b>) 300 Hz; (<b>b</b>) 311 Hz; (<b>c</b>) 334 Hz; (<b>d</b>) 359 Hz; (<b>e</b>) 388 Hz; (<b>f</b>) 404 Hz; (<b>g</b>) 451 Hz; (<b>h</b>) 494 Hz; (<b>i</b>) 503 Hz; (<b>j</b>) 537 Hz; (<b>k</b>) 565 Hz; (<b>l</b>) 609 Hz; (<b>m</b>) 652 Hz; (<b>n</b>) 676 Hz; (<b>o</b>) 736 Hz; (<b>p</b>) 783 Hz; (<b>q</b>) 826 Hz; (<b>r</b>) 874 Hz; (<b>s</b>) 894 Hz; and (<b>t</b>) 950 Hz.</p>
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<p>The distributions of the viscous power densities at the 20 marked frequency points in <a href="#materials-18-00682-f017" class="html-fig">Figure 17</a>a: (<b>a</b>) 300 Hz; (<b>b</b>) 311 Hz; (<b>c</b>) 334 Hz; (<b>d</b>) 359 Hz; (<b>e</b>) 388 Hz; (<b>f</b>) 404 Hz; (<b>g</b>) 451 Hz; (<b>h</b>) 494 Hz; (<b>i</b>) 503 Hz; (<b>j</b>) 537 Hz; (<b>k</b>) 565 Hz; (<b>l</b>) 609 Hz; (<b>m</b>) 652 Hz; (<b>n</b>) 676 Hz; (<b>o</b>) 736 Hz; (<b>p</b>) 783 Hz; (<b>q</b>) 826 Hz; (<b>r</b>) 874 Hz; (<b>s</b>) 894 Hz; and (<b>t</b>) 950 Hz.</p>
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15 pages, 5317 KiB  
Technical Note
Vertical Slowness-Constrained Joint Anisotropic Parameters and Event-Location Inversion for Downhole Microseismic Monitoring
by Congcong Yuan and Jie Zhang
Remote Sens. 2025, 17(3), 529; https://doi.org/10.3390/rs17030529 - 4 Feb 2025
Viewed by 257
Abstract
The construction of accurate anisotropic velocity models is essential for effective microseismic monitoring in hydraulic fracturing. Ignoring anisotropy can result in significant distortions in microseismic event locations and their interpretation. Although methods exist to simultaneously invert anisotropic parameters and event locations using microseismic [...] Read more.
The construction of accurate anisotropic velocity models is essential for effective microseismic monitoring in hydraulic fracturing. Ignoring anisotropy can result in significant distortions in microseismic event locations and their interpretation. Although methods exist to simultaneously invert anisotropic parameters and event locations using microseismic arrival times, the results heavily depend on accurate initial models and sufficient ray coverage due to strong trade-offs among multiple parameters. Microseismic waveform inversion for anisotropic parameters remains challenging due to the low signal-to-noise ratio of the data and the high computational cost. To address these challenges, we propose a method for jointly inverting event locations and velocity updates based on arrival times and vertical slowness estimates, under the assumption of small horizontal velocity variations. Vertical slowness estimates, which are independent of source information and easily obtainable, provide an additional constraint that enhances inversion stability. We test the proposed method in four synthetic examples under various conditions. The results demonstrate that incorporating vertical slowness effectively constrains and stabilizes conventional travel-time inversion, especially in scenarios with poor raypath coverage. Additionally, we apply this method to a field case and find that it produces more reasonable event locations compared to inversions using arrival times alone. This joint inversion method can enhance the accuracy of anisotropic structures and event locations, which thus help with fracture characterization in tight and low-permeability reservoirs. It may serve as an effective downhole monitoring approach for hydrocarbon and geothermal energy production. Full article
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<p>(<b>a</b>) The diagram of the slowness method; (<b>b</b>) the projection of the vertical slowness estimated using two receivers in the first layer of the velocity model on the theoretical slowness surface. The red circles are from the ten samples at a depth of 2000 m of the velocity model, as shown in Figure 2a.</p>
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<p>The survey geometry and inverted model results for the first case. (<b>a</b>) The velocity model includes eight layers from depth of 1700 m to 2200 m. Twelve receivers in several layers are marked by triangles. Three circles represent perforations or ball-drops at known positions. The first case is an example with three near-offset perforations or ball-drops. (<b>b</b>–<b>f</b>) The five velocity solutions are derived by two methods. The black, red, purple, and green lines included stand for initial, true, and inverted parameters by TM and VTM, respectively. The root-mean-square errors (RMSEs) of each inverted anisotropic parameter are calculated for the first six layers and are annotated for both the TM and VTM methods in the results of each model.</p>
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<p>The survey geometry and inverted model results of the second case. (<b>a</b>) The model includes eight layers from depth of 1700 m to 2200 m. Twelve receivers are marked by triangles, which are distributed in different layers. The three circles, black dots, and stars represent perforations or ball-drops with known positions (they are fixed). The second case is the example with three far-offset perforations or ball-drops. (<b>b</b>–<b>f</b>) The five velocity solutions are derived by two methods. The black, red, purple, and green lines included stand for initial, true, and inverted parameters by TM and VTM, respectively. The root-mean-square errors (RMSE) of each inverted anisotropic parameter are calculated for the first six layers and are annotated for both the TM and VTM methods in the results of each model.</p>
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<p>The survey geometry and inverted model results of the third case. (<b>a</b>) In the model, the reverse triangles are the receivers, the perforation shots are marked by a red rectangle and three stars, circles, and dots present the initial, true, and inverted locations, respectively. The purple and green represent TM and VTM method, respectively. (<b>b</b>–<b>f</b>) The inverted model results of the third case. The black, red, purple, and green lines included stand for initial, true, and inverted parameters by TM and VTM, respectively. The root-mean-square errors (RMSEs) of each inverted anisotropic parameter are calculated for the first six layers and are annotated for both the TM and VTM methods in the results of each model.</p>
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<p>The survey geometry and inverted model results of the fourth case. (<b>a</b>) In the model, the reverse triangles are the receivers, the perforation shots are marked by a red rectangle and three stars, circles, and dots present the initial, true, and inverted locations, respectively. The purple and green represent TM and VTM method, respectively. (<b>b</b>–<b>f</b>) The inverted model results of the fourth case. The black, red, purple, and green lines included stand for initial, true, and inverted parameters by TM and VTM, respectively. The root-mean-square errors (RMSEs) of each inverted anisotropic parameter are calculated for the first six layers and are annotated for both the TM and VTM methods in the results of each model.</p>
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<p>The different projections of event-location results. The left maps (<b>a</b>,<b>c</b>,<b>e</b>) show the projections of locations on X–Y, X–Z, and Y–Z using the TM, and the right ones (<b>b</b>,<b>d</b>,<b>f</b>) are the projections of locations on X–Y, X–Z, and Y–Z using the VTM. The triangle array represents the receiver array, and the black squares are ball-drops. The red dots are the event-location results of stage 3; the blue ones are the event-location results of stage 4.</p>
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<p>The inverted model results of the real case. (<b>a</b>–<b>e</b>) The five velocity solutions are derived by two methods. The black, red, purple, and green lines included stand for the initial, true, and inverted parameters by TM and VTM, respectively.</p>
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17 pages, 784 KiB  
Article
Effects of Multiplicative Noise in Bistable Dynamical Systems
by Sara C. Quintanilha Valente, Rodrigo da Costa Lima Bruni, Zochil González Arenas and Daniel G. Barci
Entropy 2025, 27(2), 155; https://doi.org/10.3390/e27020155 - 2 Feb 2025
Viewed by 352
Abstract
This study explores the escape dynamics of bistable systems influenced by multiplicative noise, extending the classical Kramers rate formula to scenarios involving state-dependent diffusion in asymmetric potentials. Using a generalized stochastic calculus framework, we derive an analytical expression for the escape rate and [...] Read more.
This study explores the escape dynamics of bistable systems influenced by multiplicative noise, extending the classical Kramers rate formula to scenarios involving state-dependent diffusion in asymmetric potentials. Using a generalized stochastic calculus framework, we derive an analytical expression for the escape rate and corroborate it with numerical simulations. The results highlight the critical role of the equilibrium potential Ueq(x), which incorporates noise intensity, stochastic prescription, and diffusion properties. We show how asymmetries and stochastic calculus prescriptions influence transition rates and equilibrium configurations. Using path integral techniques and weak noise approximations, we analyze the interplay between noise and potential asymmetry, uncovering phenomena such as barrier suppression and metastable state decay. The agreement between numerical and analytical results underscores the robustness of the proposed framework. This work provides a comprehensive foundation for studying noise-induced transitions in stochastic systems, offering insights into a broad range of applications in physics, chemistry, and biology. Full article
27 pages, 18019 KiB  
Article
Generalized Multivariate Symplectic Sparsest United Decomposition for Rolling Bearing Fault Diagnosis
by Weikang Sun, Yanfei Liu and Yanfeng Peng
Electronics 2025, 14(3), 592; https://doi.org/10.3390/electronics14030592 - 2 Feb 2025
Viewed by 313
Abstract
The non-stationary characteristics of the vibration signals of rolling bearings will be aggravated under variable speed conditions. Meanwhile, multichannel signals can provide a more comprehensive characterization of state information, providing multiple sources of information that facilitate information fusion and enhancement. However, traditional adaptive [...] Read more.
The non-stationary characteristics of the vibration signals of rolling bearings will be aggravated under variable speed conditions. Meanwhile, multichannel signals can provide a more comprehensive characterization of state information, providing multiple sources of information that facilitate information fusion and enhancement. However, traditional adaptive signal decomposition methods generally assume that the frequency information is constant and stationary, and it is difficult to achieve a unified decomposition when dealing with multichannel time-varying signals. Therefore, the intention of this paper is to propose a multichannel signal adaptive decomposition method applicable to variable speed conditions. Specifically, this paper takes advantage of the strong adaptability and robustness of symplectic geometric mode decomposition (SGMD). To improve its applicability to multichannel time-varying signals at variable rotational speeds, a generalized multivariate symplectic sparsest united decomposition (GMSSUD) method is proposed. In GMSSUD, firstly, the completely adaptive projection (CAP) method is employed to achieve a unified representation of the multichannel signals. Then, the generalized demodulation method is introduced to stabilize the signal and subsequently reduce the noise through component screening and reconstruction. Finally, with the new proposed operator as the optimization objective, the constructed sparse filter parameters are optimized to achieve the frequency band segmentation. The analysis results demonstrate that the GMSSUD method possesses higher decomposition precision for multichannel signals with variable speeds and also has a stronger diagnosis ability for variable-speed bearing faults. Full article
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<p>Schematic diagram of the CAP projection strategy.</p>
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<p>Flowchart of GMSSUD method.</p>
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<p>Schematic diagram of filter <math display="inline"><semantics> <mrow> <mi>χ</mi> <mfenced separators="|"> <mrow> <mi>k</mi> </mrow> <mrow> <mi>λ</mi> </mrow> </mfenced> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) Time-domain diagram of original components. (<b>b</b>) Time-domain diagram of multichannel simulation signals.</p>
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<p>Decomposition results of GMSSUD.</p>
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<p>Decomposition results of MESMD.</p>
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<p>Decomposition results of MVMD after fusion.</p>
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<p>Decomposition results of MEMD after fusion.</p>
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<p>The time–frequency spectrograms of multichannel simulation signals and components. (<b>a</b>) Time–frequency spectrogram of multichannel simulation signals. (<b>b</b>) Time–frequency spectrogram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>G</mi> <mi>M</mi> <mi>S</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>. (<b>c</b>) Time–frequency spectrogram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>E</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>. (<b>d</b>) Time–frequency spectrogram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>I</mi> <mi>M</mi> <mi>F</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>. (<b>e</b>) Time–frequency spectrogram of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> <mi>i</mi> <mi>m</mi> <mi>f</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) Time-domain diagram of the original components. (<b>b</b>) Time-domain diagram of multichannel variable-speed simulation fault signal.</p>
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<p>Envelope order spectra of each channel signal: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>Decomposition results of GMSSUD.</p>
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<p>Decomposition results of MESMD.</p>
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<p>Decomposition results of MVMD after fusion.</p>
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<p>Decomposition results of MEMD after fusion.</p>
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<p>Envelope order spectra of components: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>G</mi> <mi>M</mi> <mi>S</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>E</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math> (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>I</mi> <mi>M</mi> <mi>F</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>, and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> <mi>i</mi> <mi>m</mi> <mi>f</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Bearing failure test bench and experimental bearing.</p>
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<p>Rotational speed curve diagram.</p>
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<p>Time-domain diagram of three channels bearing outer ring fault vibration signals.</p>
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<p>Envelope order spectra of the corresponding signals of the three channels: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>. The circle marks in (<b>a</b>–<b>c</b>) are not obvious and are greatly disturbed by other spectral lines.</p>
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<p>The corresponding components of the four methods: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>G</mi> <mi>M</mi> <mi>S</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>2</mn> <mo>,</mo> <mn>3,1</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>E</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>7</mn> <mo>,</mo> <mn>6,5</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>I</mi> <mi>M</mi> <mi>F</mi> </mrow> <mrow> <mn>1</mn> <mo>,</mo> <mn>2,3</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> <mi>i</mi> <mi>m</mi> <mi>f</mi> </mrow> <mrow> <mn>3</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>Envelope order spectra of the corresponding components of the four methods: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>G</mi> <mi>M</mi> <mi>S</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>E</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>7</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>I</mi> <mi>M</mi> <mi>F</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> <mi>i</mi> <mi>m</mi> <mi>f</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>. Compared with (<b>b</b>–<b>d</b>), there are at most 7 obvious circle marks in (<b>a</b>), and the spacing between each circle is clear, so it can be judged that there is a fault.</p>
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<p>Rotational speed curve diagram.</p>
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<p>Time-domain diagram of three channels bearing inner ring fault vibration signals.</p>
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<p>Envelope order spectra of the corresponding signals of the three channels: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>S</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>. Only weak circle marks can be seen in the local magnification of (<b>a</b>–<b>c</b>), and the probability of failure is judged to be low.</p>
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<p>The corresponding components of the four methods: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>G</mi> <mi>M</mi> <mi>S</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>3</mn> <mo>,</mo> <mn>4,2</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>E</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>7</mn> <mo>,</mo> <mn>6,5</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>I</mi> <mi>M</mi> <mi>F</mi> </mrow> <mrow> <mn>1</mn> <mo>,</mo> <mn>2,3</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> <mi>i</mi> <mi>m</mi> <mi>f</mi> </mrow> <mrow> <mn>5</mn> <mo>,</mo> <mn>6,7</mn> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 27
<p>Envelope order spectra of the corresponding components of the four methods: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>G</mi> <mi>M</mi> <mi>S</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>E</mi> <mi>S</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow> <mn>7</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>I</mi> <mi>M</mi> <mi>F</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> <mi>i</mi> <mi>m</mi> <mi>f</mi> </mrow> <mrow> <mn>5</mn> </mrow> </msub> </mrow> </semantics></math>. There are at most 8 obvious circle marks in (<b>a</b>), and the side frequency order appears, so it can be judged that there is a fault. There are only 3 or 4 non-obvious circle marks in (<b>b</b>–<b>d</b>), and the presence of a fault cannot be judged.</p>
Full article ">
31 pages, 6403 KiB  
Article
Noise-to-Convex: A Hierarchical Framework for SAR Oriented Object Detection via Scattering Keypoint Feature Fusion and Convex Contour Refinement
by Shuoyang Liu, Ming Tong, Bokun He, Jiu Jiang and Chu He
Electronics 2025, 14(3), 569; https://doi.org/10.3390/electronics14030569 - 31 Jan 2025
Viewed by 361
Abstract
Oriented object detection has become a hot topic in SAR image interpretation. Due to the unique imaging mechanism, SAR objects are represented as clusters of scattering points surrounded by coherent speckle noise, leading to blurred outlines and increased false alarms in complex scenes. [...] Read more.
Oriented object detection has become a hot topic in SAR image interpretation. Due to the unique imaging mechanism, SAR objects are represented as clusters of scattering points surrounded by coherent speckle noise, leading to blurred outlines and increased false alarms in complex scenes. To address these challenges, we propose a novel noise-to-convex detection paradigm with a hierarchical framework based on the scattering-keypoint-guided diffusion detection transformer (SKG-DDT), which consists of three levels. At the bottom level, the strong-scattering-region generation (SSRG) module constructs the spatial distribution of strong scattering regions via a diffusion model, enabling the direct identification of approximate object regions. At the middle level, the scattering-keypoint feature fusion (SKFF) module dynamically locates scattering keypoints across multiple scales, capturing their spatial and structural relationships with the attention mechanism. Finally, the convex contour prediction (CCP) module at the top level refines the object outline by predicting fine-grained convex contours. Furthermore, we unify the three-level framework into an end-to-end pipeline via a detection transformer. The proposed method was comprehensively evaluated on three public SAR datasets, including HRSID, RSDD-SAR, and SAR-Aircraft-v1.0. The experimental results demonstrate that the proposed method attains an AP50 of 86.5%, 92.7%, and 89.2% on these three datasets, respectively, which is an increase of 0.7%, 0.6%, and 1.0% compared to the existing state-of-the-art method. These results indicate that our approach outperforms existing algorithms across multiple object categories and diverse scenes. Full article
(This article belongs to the Section Artificial Intelligence)
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