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Search Results (1,449)

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21 pages, 2186 KiB  
Article
Damage Status and Failure Precursors of Different Coal Impact Types Based on Comprehensive Monitoring of Infrared Radiation and Acoustic Emission
by Shan Yin, Zhonghui Li, Enyuan Wang, Yubing Liu, Yue Niu and Hengze Yang
Appl. Sci. 2024, 14(19), 8792; https://doi.org/10.3390/app14198792 (registering DOI) - 29 Sep 2024
Abstract
Different coal failure impact types exhibit different damage statuses and failure modes, resulting in distinct signal characteristics of infrared radiation (IR) and acoustic emission (AE). This paper combines IR and AE monitoring methods to innovatively establish coal damage and failure precursor warning models [...] Read more.
Different coal failure impact types exhibit different damage statuses and failure modes, resulting in distinct signal characteristics of infrared radiation (IR) and acoustic emission (AE). This paper combines IR and AE monitoring methods to innovatively establish coal damage and failure precursor warning models and obtains the IR and AE precursor characteristics for different coal failure impact types. This research shows that there is a good correspondence between IR and AE timing and spatial distribution of different coal impact types. As the impact tendency increases, the intensity of IR and AE signals increases with coal failure, and the AE positioning points and IR high-temperature areas tend to concentrate. The coal body gradually changes from tensile failure to shear failure. The shear cracks in the failure stage of coal with no, weak, and strong impact are 39.9%, 50.9%, and 53.7%, respectively. The IR and AE instability precursor point of coal with no, weak, and strong impact occurred at 55.2%, 66.3%, and 93.4% of coal failure, respectively. After the IR and AE combined instability precursor point, the dissipated energy and combined damage variable increase rapidly, and the coal body will undergo instability and failure. The research results provide a theoretical basis for comprehensive monitoring of coal body failure and rock burst. Full article
23 pages, 21133 KiB  
Article
Data-Driven Feature Extraction-Transformer: A Hybrid Fault Diagnosis Scheme Utilizing Acoustic Emission Signals
by Chenggong Ma, Jiuyang Gao, Zhenggang Wang, Ming Liu, Jing Zou, Zhipeng Zhao, Jingchao Yan and Junyu Guo
Processes 2024, 12(10), 2094; https://doi.org/10.3390/pr12102094 - 26 Sep 2024
Abstract
This paper introduces a novel network, DDFE-Transformer (Data-Driven Feature Extraction-Transformer), for fault diagnosis using acoustic emission signals. The DDFE-Transformer network integrates two primary modules: the DDFE module, focusing on noise reduction and feature enhancement, and the Transformer module. The DDFE module employs two [...] Read more.
This paper introduces a novel network, DDFE-Transformer (Data-Driven Feature Extraction-Transformer), for fault diagnosis using acoustic emission signals. The DDFE-Transformer network integrates two primary modules: the DDFE module, focusing on noise reduction and feature enhancement, and the Transformer module. The DDFE module employs two techniques: the Wavelet Kernel Network (WKN) for noise reduction and the Convolutional Block Attention Module (CBAM) for feature enhancement. The wavelet function in the WKN reduces noise, while the attention mechanism in the CBAM enhances features. The Transformer module then processes the feature vectors and sends the results to the softmax layer for classification. To validate the proposed method’s efficacy, experiments were conducted using acoustic emission datasets from NASA Ames Research Center and the University of California, Berkeley. The results were compared using the four key metrics obtained through confusion matrix analysis. Experimental results show that the proposed method performs excellently in fault diagnosis using acoustic emission signals, achieving a high average accuracy of 99.84% and outperforming several baseline models, such as CNN, CNN-LSTM, CNN-GRU, VGG19, and ZFNet. The best-performing model, VGG19, only achieved an accuracy of 88.61%. Additionally, the findings suggest that integrating noise reduction and feature enhancement in a single framework significantly improves the network’s classification accuracy and robustness when analyzing acoustic emission signals. Full article
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<p>Transition in structure from CNN to WKN.</p>
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<p>The structure of CBAM model.</p>
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<p>Position encoding and encoders using Transformer.</p>
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<p>Structure of the self-attention mechanism.</p>
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<p>Multiple attention mechanisms.</p>
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<p>The flowchart of the proposed fault diagnosis method.</p>
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<p>Schematic of the experimental setup and tool wear.</p>
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<p>Visualization of acoustic emission signals.</p>
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<p>Data augmentation.</p>
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<p>Model performance on training and validation sets.</p>
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<p>ROC curve of DDFE-Transformer.</p>
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<p>Metrics in ablation experiment (<b>a</b>) <span class="html-italic">Accuracy</span>, (<b>b</b>) <span class="html-italic">Precision</span>, (<b>c</b>) <span class="html-italic">Recall</span>, (d) <span class="html-italic">F</span>1 score.</p>
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<p>Matrix of confusion for each of the models of the ablation experiment.</p>
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<p>t-SNE plots for each model of the ablation experiment.</p>
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<p>Metrics in comparison experiment (<b>a</b>) <span class="html-italic">Accuracy</span>, (<b>b</b>) <span class="html-italic">Precision</span>, (<b>c</b>) <span class="html-italic">Recall</span>, (<b>d</b>) <span class="html-italic">F</span>1 score.</p>
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<p>Accuracy of different models.</p>
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<p>Matrix of confusion for each of the models of the comparison experiment.</p>
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<p>t-SNE plots for each model of the comparison experiment.</p>
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21 pages, 10339 KiB  
Article
The Integration of Bio-Active Elements into Building Façades as a Sustainable Concept
by Walaa Mohamed Metwally and Vitta Abdel Rehim Ibrahim
Buildings 2024, 14(10), 3086; https://doi.org/10.3390/buildings14103086 - 26 Sep 2024
Abstract
Global warming and climate change are major concerns across multiple disciplines. Population growth, urbanization, and industrialization are significant contributing factors to such problems due to the escalating use of fossil fuels required to meet growing energy demands. The building sector uses the largest [...] Read more.
Global warming and climate change are major concerns across multiple disciplines. Population growth, urbanization, and industrialization are significant contributing factors to such problems due to the escalating use of fossil fuels required to meet growing energy demands. The building sector uses the largest share of total global energy production and produces tons of greenhouse gas emissions. Emerging eco-friendly technologies, such as solar and wind energy harvesting, are being extensively explored; however, they are insufficient. Nature-inspired technologies could offer solutions to our problems. For instance, algae are microorganisms that use water, light, and CO2 to produce energy and sustain life, and the exploitation of these characteristics in a built environment is termed algae building technology, which is a very efficient and green application suitable for a sustainable future. Algae-integrated façades show great versatility through biomass and energy production, wastewater treatment, shading, and thermal and acoustic insulation. In this paper, algae will be introduced as a robust tool toward a greener and more sustainable future. Algae building technology and its implementation will be demonstrated. Furthermore, steps for applying this sustainable strategy in Egypt will be discussed. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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<p>Life cycle of algae [<a href="#B21-buildings-14-03086" class="html-bibr">21</a>]: <a href="https://sciencing.com" target="_blank">https://sciencing.com</a>.</p>
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<p>A schematic elucidating the inputs and outputs of an algae-powered building and their use [<a href="#B14-buildings-14-03086" class="html-bibr">14</a>].</p>
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<p>A schematic showing the flow of bioenergy and biomass production [<a href="#B1-buildings-14-03086" class="html-bibr">1</a>].</p>
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<p>Elucidative demonstration for the application of algae technology [<a href="#B31-buildings-14-03086" class="html-bibr">31</a>].</p>
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<p>Maps of Muhammad Ali Palace and surrounded areas, Egypt (Google Maps).</p>
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<p>Interview sample (by: authors).</p>
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<p>Main positive key aspects (by: authors).</p>
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<p>Steps of implementation (developed by the authors).</p>
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24 pages, 4109 KiB  
Review
A Review of Acoustic Emission Source Localization Techniques in Different Dimensions
by Alipujiang Jierula, Cong Wu, Abudusaimaiti Kali and Zhixuan Fu
Appl. Sci. 2024, 14(19), 8684; https://doi.org/10.3390/app14198684 - 26 Sep 2024
Abstract
Acoustic emission (AE) source localization technology, since the early application to one-dimensional structures, has been extended to a wide range of applications to two-dimensional (2D) structures, including isotropic and anisotropic materials, which are currently the most widely studied and the most mature. With [...] Read more.
Acoustic emission (AE) source localization technology, since the early application to one-dimensional structures, has been extended to a wide range of applications to two-dimensional (2D) structures, including isotropic and anisotropic materials, which are currently the most widely studied and the most mature. With the development of AE source localization technology, more and more significant challenges have arisen for three-dimensional (3D) structures, which are mostly anisotropic and have complex propagation paths. This paper summarizes and discusses the AE source localization methods in different dimensions as well as their applications, including the main methods for 2D AE source localization, such as the triangulation method, beam forming, strain rosette technique, modal AE, artificial neural network, optimization and the time reversal technique, as well as state-of-the-art AE source localization methods in isotropic and anisotropic structures utilizing these methods. Recent advances in AE source localization in complex 3D structures are also reviewed. Full article
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<p>One-dimensional time difference methods.</p>
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<p>Method for 2D sound source localization.</p>
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<p>Triangular time difference localization method.</p>
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<p>Positioning methods based on time difference method: (<b>a</b>) rhombic AE localization method [<a href="#B3-applsci-14-08684" class="html-bibr">3</a>]; (<b>b</b>) normalized square localization method [<a href="#B4-applsci-14-08684" class="html-bibr">4</a>]; (<b>c</b>) planar square–triangle localization method [<a href="#B3-applsci-14-08684" class="html-bibr">3</a>]; (<b>d</b>) triangular time-difference localization method with known velocity.</p>
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<p>Four-sensor beam forming technique.</p>
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<p>(<b>a</b>) Beam forming localization method [<a href="#B22-applsci-14-08684" class="html-bibr">22</a>]. (<b>b</b>) Beam forming localization method using L-shaped sensor array.</p>
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<p>(<b>a</b>) Rosette array localization method. (<b>b</b>) Localization method using six sensors. (<b>c</b>) Three closely placed AE sensors for AE source localization.</p>
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<p>(<b>a</b>) AE source localization method with rhombic wavefront [<a href="#B41-applsci-14-08684" class="html-bibr">41</a>]. (<b>b</b>) AE source localization method with elliptical wavefront.</p>
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<p>Method for 3D sound source localization.</p>
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<p>Time difference positioning method in three-dimensional structure.</p>
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<p>In situ retrofitted RC beam test. (<b>a</b>) Scheme of the beam cross-section. (<b>b</b>) Photo of a flexural crack in between transducers 3 and 4 (using an optical microscopy with magnification 100×). (<b>c</b>) Scheme of the beam indicating localized AE sources. (<b>d</b>) AE counting number for each sensor Si during the loading test. (<b>e</b>) The b-value during the loading test.</p>
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<p>3D structural sound source localization based on AIC.</p>
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<p>Schematic of three-dimensional location of cube monitoring network: (<b>a</b>) AE sensors at A, B, C, D, E; (<b>b</b>) AE sensors at A, B, C, D, H; (<b>c</b>) AE sensors at A, B, C, D, G; (<b>d</b>) AE sensors at A, B, C, D, F.</p>
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17 pages, 23803 KiB  
Article
Experimental Study on Acoustic Emission Features and Energy Dissipation Properties during Rock Shear-Slip Process
by Zhengnan Zhang, Xiangxin Liu, Kui Zhao, Zhengzhao Liang, Bin Gong and Xun You
Materials 2024, 17(19), 4684; https://doi.org/10.3390/ma17194684 - 24 Sep 2024
Abstract
The features of rock shear-slip fracturing are closely related to the stability of rock mass engineering. Granite, white sandstone, red sandstone, and yellow sandstone specimens were selected in this study. The loading phase of “shear failure > slow slip > fast slip” was [...] Read more.
The features of rock shear-slip fracturing are closely related to the stability of rock mass engineering. Granite, white sandstone, red sandstone, and yellow sandstone specimens were selected in this study. The loading phase of “shear failure > slow slip > fast slip” was set up to explore the correlation between fracture type, acoustic emission (AE) features, and energy dissipation during the rock fracturing process. The results show that there is a strong correlation between fracture type, energy dissipation, and AE features. The energy dissipation ratio of tension-shear (T-S) composite, shear, and tensile types is 10:100:1. The fracture types in the shear failure phase are mainly tensile and TS composite types. The differential mechanism of energy dissipation of different rocks during the shear-slip process is revealed from the physical property perspectives of mineral composition, particle size, and diagenetic mode. These results provide a necessary research basis for energy dissipation research in rock failure and offer an important scientific foundation for analyzing the fracture propagation problem in the shear-slip process. They also provide a research basis for further understanding the acoustic emission characteristics and crack type evolution during rock shear and slip processes, which helps to better understand the shear failure mechanism of natural joints and provides a reference for the identification of precursors of shear disasters in geotechnical engineering. Full article
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<p>Schematic diagram of the loading mode and the position of AE sensors. (<b>a</b>), The loading mode of specimens, the orange arrow in the horizontal direction represents the shear load, and the blue arrow in the vertical direction represents the normal load. (<b>b</b>), The position of AE sensors, the circle with number 1–8 represents the position of all AE sensors.</p>
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<p>Rock specimen. ((<b>a</b>), RSLT-1, granite; (<b>b</b>), RSLT-3, white sandstone; (<b>c</b>), RSLT-4,red sandstone; (<b>d</b>), RSLT-5, yellow Sandstone).</p>
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<p>Diagram of test setup.</p>
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<p>Schematic diagram of normal and shear loading paths.</p>
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<p>Mechanical curve of shear stress in rock shear-slip test. ((<b>a</b>), Shear load-time curve; (<b>b</b>), Shear stress-shear strain curve in shear failure phase).</p>
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<p>Failure morphology of rock specimens. (RSLT-1 is a granite specimen, RSLT-3 is a white sandstone specimen, RSLT-4 is a red sandstone specimen, RSLT-5 is a yellow sandstone specimen).</p>
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<p>Cumulative AE energy, counting, and time curves of rock fracturing process. ((<b>a</b>), RSLT-1; (<b>b</b>), RSLT-3; (<b>c</b>), RSLT-4; (<b>d</b>), RSLT-5).</p>
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<p>Distribution and proportion of fracturing types and their proportions during the loading process of RSLT-1. (From left to right: shear failure, slow slip, and fast slip phases).</p>
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<p>Distribution and proportion of fracturing types and their proportions during the loading process of RSLT-3. (From left to right, shear failure, slow slip, and fast slip phases).</p>
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<p>Distribution and proportion of fracturing types and their proportions during the loading process of RSLT-4. (From left to right: shear failure, slow slip, and fast slip phases).</p>
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<p>Distribution and proportion of fracturing types and their proportions during the loading process of RSLT-5. (From left to right: shear failure, slow slip, and fast slip phases).</p>
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<p>Relationship between shear load, AE energy, fracture propagation, and time during the shear-slip process. (<b>a</b>), RSLT-1; (<b>b</b>), RSLT-3; (<b>c</b>), RSLT-4; (<b>d</b>), RSLT-5. I–III in the figure represent the shear failure phase, the slow slip phase and the fast slip phase, respectively.</p>
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<p>Relationship between fracture type and AE energy level of different rock specimens during the shear-slip process. (<b>a</b>), RSLT-1; (<b>b</b>), RSLT-3; (<b>c</b>), RSLT-4; (<b>d</b>), RSLT-5.</p>
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<p>Schematic diagram of macro-meso-micro scale fractures on slip crack surface. The arrows in the figure represent the rotation state of rock particles under horizontal shear load.</p>
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30 pages, 21758 KiB  
Article
Study of Acoustic Emission Signal Noise Attenuation Based on Unsupervised Skip Neural Network
by Tuoya Wulan, Guodong Li, Yupeng Huo, Jiangjiang Yu, Ruiqi Wang, Zhongzheng Kou and Wen Yang
Sensors 2024, 24(18), 6145; https://doi.org/10.3390/s24186145 - 23 Sep 2024
Abstract
Acoustic emission (AE) technology, as a non-destructive testing methodology, is extensively utilized to monitor various materials’ structural integrity. However, AE signals captured during experimental processes are often tainted with assorted noise factors that degrade the signal clarity and integrity, complicating precise analytical evaluations [...] Read more.
Acoustic emission (AE) technology, as a non-destructive testing methodology, is extensively utilized to monitor various materials’ structural integrity. However, AE signals captured during experimental processes are often tainted with assorted noise factors that degrade the signal clarity and integrity, complicating precise analytical evaluations of the experimental outcomes. In response to these challenges, this paper introduces an unsupervised deep learning-based denoising model tailored for AE signals. It juxtaposes its efficacy against established methods, such as wavelet packet denoising, Hilbert transform denoising, and complete ensemble empirical mode decomposition with adaptive noise denoising. The results demonstrate that the unsupervised skip autoencoder model exhibits substantial potential in noise reduction, marking a significant advancement in AE signal processing. Subsequently, the paper focuses on applying this advanced denoising technique to AE signals collected during the tensile testing of steel fiber-reinforced concrete (SFRC), the tensile testing of steel, and flexural experiments of reinforced concrete beam, and it meticulously discusses the variations in the waveform and the spectrogram of the original signal and the signal after noise reduction. The results show that the model can also remove the noise of AE signals. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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<p>Model diagram.</p>
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<p>Time-domain waveforms and spectral diagrams of simulated AE signals and noisy AE signals. (<b>a</b>) Waveform diagram of the simulated AE signal; (<b>b</b>) Waveform diagram of the simulated AE signal with noisy; (<b>c</b>) Spectrum diagram of the simulated AE signal; (<b>d</b>) Spectrum diagram of the simulated AE signal with noisy.</p>
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<p>Time-domain waveforms and spectral diagrams of simulated AE signals, noisy AE signals, and denoise AE signal by the wavelet packet. (<b>a</b>) Waveforms of the AE signal and denoise AE signal; (<b>b</b>) Waveforms of the AE signal with noisy and denoise AE signal; (<b>c</b>) Spectral diagram of the AE signal and denoise AE signals. (<b>d</b>) Spectral diagram of the AE signal with noisy and denoise AE signals.</p>
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<p>Time-domain waveforms and spectral diagrams of simulated AE signals, noisy AE signals, and denoise AE signals by HHT. (<b>a</b>) Waveforms of AE signal and denoise AE signal. (<b>b</b>) Waveforms of AE signal with noisy and denoise AE signal. (<b>c</b>) Spectral diagrams of AE signal and denoise AE signal. (<b>d</b>) Spectral diagrams of AE signal with noisy and denoise AE signal.</p>
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<p>Time-domain waveforms and spectral diagrams of simulated AE signals, noisy AE signals, and denoise AE signals by HHT. (<b>a</b>) Waveforms of AE signal and denoise AE signal. (<b>b</b>) Waveforms of AE signal with noisy and denoise AE signal. (<b>c</b>) Spectral diagrams of AE signal and denoise AE signal. (<b>d</b>) Spectral diagrams of AE signal with noisy and denoise AE signal.</p>
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<p>Diagram of CEEMDAN decomposition.</p>
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<p>Time-domain waveforms and spectral diagrams of simulated AE signals, noisy AE signals, and denoise AE signals by CEEMDAN. (<b>a</b>) Waveforms of the AE signal and denoise AE signal; (<b>b</b>) Waveforms of the AE signal with noisy and the denoise AE signal; (<b>c</b>) Spectral diagrams of the AE signal and denoise AE signal; (<b>d</b>) Spectral diagrams of the AE signal with noisy and the denoise AE signal.</p>
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<p>Time-domain waveforms and spectral diagrams of simulated AE signals, noisy AE signals, and denoise AE signals by USAM and MSE. (<b>a</b>) Waveforms of the AE signal and denoise AE signal; (<b>b</b>) Waveforms of the AE signal with noisy and the denoise AE signal; (<b>c</b>) Spectral diagrams of the AE signal and denoise AE signal; (<b>d</b>) Spectral diagrams of the AE signal with noisy and the denoise AE signal.</p>
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<p>Time-domain waveforms and spectral diagrams of simulated AE signals and denoise AE signals by USAM and Welsch loss. (<b>a</b>) Waveforms of the AE signal and the denoise AE signal; (<b>b</b>) Spectral diagrams of the AE signal with noisy and the denoise AE signal.</p>
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<p>Experimental procedure and sensor layout. (<b>a</b>) Experimental procedure; (<b>b</b>) Experimental procedure; (<b>c</b>) Arrangement of the sensors.</p>
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<p>Diagram of the specimen dimensions and the arrangement of the acoustic emission sensors.</p>
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<p>Tensile testing schematic and experimental procedure. (<b>a</b>) Tensile testing schematic; (<b>b</b>) Experimental procedure.</p>
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<p>Analysis of SNR. The dimensions of the RC beam and the arrangement of the AE sensors.</p>
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<p>Test setup.</p>
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<p>Training and validation loss curves of SFRC. (<b>a</b>) Specimen K1; (<b>b</b>) Specimen K2; (<b>c</b>) Specimen K3.</p>
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<p>Training and validation loss curves of steel tensile. (<b>a</b>) Specimen S1; (<b>b</b>) Specimen S2; (<b>c</b>) Specimen S3.</p>
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<p>Training and validation loss curves of the reinforced concrete beam flexural. (<b>a</b>) Specimen F1; (<b>b</b>) Specimen F2; (<b>c</b>) Specimen F3.</p>
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<p>Time-domain waveforms and spectral diagrams of noisy AE signals and denoise AE signals of SFRC. (<b>a</b>) AE signal and denoise AE signal; (<b>b</b>) AE signal; (<b>c</b>) Denoise AE signal; (<b>d</b>) AE signal and denoise AE signal.</p>
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<p>Time-domain waveforms and spectral diagrams of noisy AE signals and denoise AE signals. (<b>a</b>) AE signal and denoise AE signal; (<b>b</b>) AE signal; (<b>c</b>) Denoise AE signal; (<b>d</b>) AE signal and denoise AE signal.</p>
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<p>Time-domain waveforms and spectral diagrams of noisy AE signals and denoise AE signals. (<b>a</b>) AE signal and denoise AE signal; (<b>b</b>) AE signal; (<b>c</b>) Denoise AE signal; (<b>d</b>) AE signal and denoise AE signal.</p>
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19 pages, 8508 KiB  
Article
A Proposed Algorithm Based on Variance to Effectively Estimate Crack Source Localization in Solids
by Young-Chul Choi, Byunyoung Chung and Doyun Jung
Sensors 2024, 24(18), 6092; https://doi.org/10.3390/s24186092 - 20 Sep 2024
Abstract
Acoustic emissions (AEs) are produced by elastic waves generated by damage in solid materials. AE sensors have been widely used in several fields as a promising tool to analyze damage mechanisms such as cracking, dislocation movement, etc. However, accurately determining the location of [...] Read more.
Acoustic emissions (AEs) are produced by elastic waves generated by damage in solid materials. AE sensors have been widely used in several fields as a promising tool to analyze damage mechanisms such as cracking, dislocation movement, etc. However, accurately determining the location of damage in solids in a non-destructive manner is still challenging. In this paper, we propose a crack wave arrival time determination algorithm that can identify crack waves with low SNRs (signal-to-noise ratios) generated in rocks. The basic idea is that the variances in the crack wave and noise have different characteristics, depending on the size of the moving window. The results can be used to accurately determine the crack source location. The source location is determined by observing where the variance in the crack wave velocities of the true and imaginary crack location reach a minimum. By performing a pencil lead break test using rock samples, it was confirmed that the proposed method could successfully find wave arrival time and crack localization. The proposed algorithm for source localization can be used for evaluating and monitoring damage in tunnels or other underground facilities in real time. Full article
(This article belongs to the Section Physical Sensors)
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<p>A crack wave generated in rock. The sampling frequency is 500 kHz and the number of data points is 4096. It is difficult to determine the arrival time of the p-wave in the presence of the ambient noise signal.</p>
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<p>The frequency analysis results obtained from the <a href="#sensors-24-06092-f001" class="html-fig">Figure 1</a> signal. (<b>a</b>) Power spectrum for a crack wave and (<b>b</b>) power spectrum for background noise. In the frequency characteristics, we can observe that a crack wave has a narrow band, and the noise has a broad band.</p>
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<p>Signal variance according to window size for (<b>a</b>) noise signal and (<b>b</b>) crack wave.</p>
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<p>Proposed algorithm for determining the crack wave arrival time. While calculating the variance during window resizing, the point (the red arrow on the right) where the variances are different is the arrival time of the crack wave.</p>
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<p>Results from applying the proposed method, assuming the crack wave is a sine wave. (<b>a</b>) Sine wave signal and (<b>b</b>) the variance in the sine wave using Equations (4) and (8). Because the rate of change in the variance is large within one wavelength of the signal, the window size should be larger than one wavelength.</p>
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<p>Concept explanation for source localization. If the velocities are calculated while scanning an image source, two velocities will match at the location of the true source.</p>
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<p>A schematic diagram of the pencil lead break experiment to test the accuracy of the method for source localization. (<b>a</b>) Location of the AE sensors and excitation points on the granite rock and (<b>b</b>) picture of the experimental setup.</p>
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<p>AE sensors and instruments used in this test. (<b>a</b>) AE-300 and (<b>b</b>) AE-603 SW-GA sensor.</p>
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<p>Measured AE signals when the pencil lead break test was performed at excitation point 1. Depending on the sensor locations, there is a difference in signal arrival delay.</p>
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<p>Experimental results using the proposed moving window method when the pencil lead break test was performed at excitation point 1. We can easily find the starting point (the black arrow) at which the variances in the measured signal change as the window size changes.</p>
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<p>Source location was estimated by calculating the variance in velocities; the minimum value of variance indicates the source location. The estimated source location was (125.8 mm, 2.7 mm), while the true source location was (125 mm, 0 mm).</p>
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<p>Source location was estimated by calculating the variance in velocities; the minimum value of variance indicates the source location. The estimated source location was (−0.5 mm, 0.5 mm), while the true source location was (0 mm, 0 mm).</p>
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<p>Source location was estimated by calculating the variance in velocities; the minimum value of variance indicates the source location. The estimated source location was (−0.5 mm, 0.5 mm), while the true source location was (0 mm, 0 mm).</p>
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<p>Source location was estimated by calculating the variance in velocities; the minimum value of variance indicates the source location. The estimated source location was (−124.7 mm, 1.5 mm), while the true source location was (−125 mm, 0 mm).</p>
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<p>The signals were a mixture of artificial noise and <a href="#sensors-24-06092-f009" class="html-fig">Figure 9</a> signals when the pencil lead break test was performed at excitation point 1. Noise makes it more difficult to find the starting point of the crack signal.</p>
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<p>Experimental results in a noisy environment when the pencil lead break test was performed at excitation point 1. The black arrows mean the arrival times of crack wave. Applying the proposed method makes it easy to find the starting point of the crack signal even in a noisy environment.</p>
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<p>The source localization result. The estimated source location was (−124.7 mm, 0.5 mm) when the true source location was (−125 mm, 0 mm).</p>
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<p>KURT (Korea Underground Research Tunnel) and research module.</p>
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<p>(<b>a</b>) Location of AE sensors and excitation points on the ground of the tunnel and (<b>b</b>) experimental pictures.</p>
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<p>(<b>a</b>) Signal results from each sensor and (<b>b</b>) calculation of moving window when Exc. Point 1 was excited with an impact hammer. The black arrows mean the arrival time of impact wave.</p>
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<p>The result of the estimated impact location when Exc. Point 1 location is (x, y) = (−0.25 m, 0.25 m). (<b>a</b>) The estimated location applying the time delay obtained by the conventional method is (x, y) = (0 m, 0.399 m). (<b>b</b>) The estimated location applying the time delay obtained by the proposed method is (x, y) = (−0.267 m, 0.248 m). The blue dots represent sensor locations and X represents the excitation point.</p>
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<p>The result of the estimated impact location when Exc. Point 1 location is (x, y) = (−0.25 m, 0.25 m). (<b>a</b>) The estimated location applying the time delay obtained by the conventional method is (x, y) = (0 m, 0.399 m). (<b>b</b>) The estimated location applying the time delay obtained by the proposed method is (x, y) = (−0.267 m, 0.248 m). The blue dots represent sensor locations and X represents the excitation point.</p>
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<p>The result of the estimated impact location when Exc. Point 1 location is (x, y) = (1 m, −0.5 m). (<b>a</b>) The estimated location applying the time delay obtained by the conventional method is (x, y) = (−0.09 m, −0.49 m). (<b>b</b>) The estimated location applying the time delay obtained by the proposed method is (x, y) = (0.98 m, −0.52 m). The blue dots represent sensor locations and X represents the excitation point.</p>
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<p>The result of the estimated impact location when Exc. Point 1 location is (x, y) = (1 m, −0.5 m). (<b>a</b>) The estimated location applying the time delay obtained by the conventional method is (x, y) = (−0.09 m, −0.49 m). (<b>b</b>) The estimated location applying the time delay obtained by the proposed method is (x, y) = (0.98 m, −0.52 m). The blue dots represent sensor locations and X represents the excitation point.</p>
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16 pages, 9368 KiB  
Article
A Method for the Pattern Recognition of Acoustic Emission Signals Using Blind Source Separation and a CNN for Online Corrosion Monitoring in Pipelines with Interference from Flow-Induced Noise
by Xueqin Wang, Shilin Xu, Ying Zhang, Yun Tu and Mingguo Peng
Sensors 2024, 24(18), 5991; https://doi.org/10.3390/s24185991 - 15 Sep 2024
Abstract
As a critical component in industrial production, pipelines face the risk of failure due to long-term corrosion. In recent years, acoustic emission (AE) technology has demonstrated significant potential in online pipeline monitoring. However, the interference of flow-induced noise seriously hinders the application of [...] Read more.
As a critical component in industrial production, pipelines face the risk of failure due to long-term corrosion. In recent years, acoustic emission (AE) technology has demonstrated significant potential in online pipeline monitoring. However, the interference of flow-induced noise seriously hinders the application of acoustic emission technology in pipeline corrosion monitoring. Therefore, a pattern-recognition model for online pipeline AE monitoring signals based on blind source separation (BSS) and a convolutional neural network (CNN) is proposed. First, the singular spectrum analysis (SSA) was employed to transform the original AE signal into multiple observed signals. An independent component analysis (ICA) was then utilized to separate the source signals from the mixed signals. Subsequently, the Hilbert–Huang transform (HHT) was applied to each source signal to obtain a joint time–frequency domain map and to construct and compress it. Finally, the mapping relationship between the pipeline sources and AE signals was established based on the CNN for the precise identification of corrosion signals. The experimental data indicate that when the average amplitude of flow-induced noise signals is within three times that of corrosion signals, the separation of mixed signals is effective, and the overall recognition accuracy of the model exceeds 90%. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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<p>The proposed online model for monitoring pipeline corrosion.</p>
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<p>Schematic diagram of the pipeline test bench structure. (<b>a</b>) Schematic diagram of the experimental simplification; (<b>b</b>) Pipeline corrosion monitoring experimental platform; (<b>c</b>) Schematic diagram of the flow-induced noise interference; (<b>d</b>) Workflow diagram for data acquisition and processing.</p>
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<p>Time–frequency analysis of the original signals. (<b>a</b>) Waveforms of three types of signals; (<b>b</b>) spectrograms of three types of signals; (<b>c</b>) power spectra of flow-induced noise at different flow velocities.</p>
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<p>Blind source separation results for mixed signals at different flow velocities. (<b>a</b>) Separated waveforms; (<b>b</b>) kurtosis values for each IC.</p>
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<p>Construction of time–frequency feature maps for signals. (<b>a</b>) Original waveforms of corrosion signals, flow-induced noise, and separated waveforms of mixed signals; (<b>b</b>) Hilbert spectra of three types of signals; (<b>c</b>) compressed signal feature map.</p>
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<p>Accuracy graph of the SSA-ICA-CNN model iterations at different flow rates.</p>
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<p>Recognition results at different flow rates. (<b>a</b>) Confusion matrices of model recognition results at various flow rates (The blue color is the correct recognition result, and darker blue indicates more correct recognition result. The orange color is the error recognition result, and darker orange indicates more error recognition result.); (<b>b</b>) recognition accuracy of mixed signals at different flow rates.</p>
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<p>Accuracy of VMD-CNN model iterations at different flow rates.</p>
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<p>Performance comparison of different hyperparametric networks.</p>
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16 pages, 5633 KiB  
Article
Surrounding Rock Control Technology of Thick Hard Roof and Hard Coal Seam Roadway under Tectonic Stress
by Zhongzong Cao, Honglin Liu, Chengfang Shan, Hongzhi Wang and Haitong Kang
Processes 2024, 12(9), 1973; https://doi.org/10.3390/pr12091973 - 13 Sep 2024
Abstract
In the process of roadway excavation in thick and hard coal seams with a hard roof, the instantaneous release of a large amount of elastic energy accumulated in coal and rock mass causes disasters. Especially under the action of tectonic stress, dynamic disasters [...] Read more.
In the process of roadway excavation in thick and hard coal seams with a hard roof, the instantaneous release of a large amount of elastic energy accumulated in coal and rock mass causes disasters. Especially under the action of tectonic stress, dynamic disasters of roadway-surrounding rock are extremely strong. Therefore, this paper takes the 110,505 roadway of the Yushuling Coal Mine as the engineering background. Aiming at the serious deformation of roadway-surrounding rock and the problem of strong mine pressure, the deformation mechanism of roadway-surrounding rock is studied by means of theoretical analysis, indoor experimentation, numerical simulation and field testing, and the surrounding rock control technology is proposed. Firstly, the results show that the stress field type of the Yushuling Coal Mine is a σHv type, the azimuth angle of the maximum horizontal principal stress is concentrated in 110.30°~114.12°, the dip angle is −33.04°~−3.43°, and the maximum horizontal principal stress is 1.94~2.76 times of the minimum horizontal principal stress. Secondly, the brittleness index of No. 5 is 0.62; the failure energy release of the surrounding rock compressive energy floor rock sample is up to 150,000 mv * ms. The more the cumulative number of rock samples, the greater the strength, and the more severe the damage. Thirdly, with the increase in tectonic stress, the stress of roadway-surrounding rock is asymmetrically distributed, and the plastic zone develops along the tendency. The maximum range of the plastic zone expands from 4.18 m to 10.19 m. Lastly, according to the deformation characteristics of roadway-surrounding rock, left side > roof > right side > floor, the surrounding rock control technology of ‘asymmetric anchor net cable support + borehole pressure relief’ is proposed, which realizes the effective control of roadway-surrounding rock deformation. Full article
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<p>No.5 Coal seam and roof and floor histogram.</p>
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<p>In-situ stress measuring point layout diagram of hollow core inclusion.</p>
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<p>E45.605 mine rock mechanical properties test system.</p>
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<p>The orientation relationship between the direction of in situ stress and the 110,505 headentry.</p>
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<p>No. 5 Coal sample stress–strain curve.</p>
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<p>Acoustic emission ringing count and energy evolution law of No. 5 coal roof and floor rock samples.</p>
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<p>Construction of numerical calculation model of surrounding rock strata in 110,505 headentry roadway.</p>
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<p>Horizontal stress nephogram of surrounding rock of 110,505 headentry under different tectonic stress.</p>
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<p>Vertical stress nephogram of surrounding rock of 110,505 transportation roadway under different tectonic stress.</p>
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<p>Cloud diagrams of plastic zone of surrounding rock of the 110,505 transportation roadway under different tectonic stress.</p>
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<p>Surrounding rock control technology of the 110,505 roadway combined with an ‘asymmetric anchor net cable + pressure relief hole’.</p>
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<p>Surrounding rock control technology of the 110,505 roadway combined with an ‘asymmetric anchor net cable + pressure relief hole’.</p>
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<p>Deformation monitoring of surrounding rock of 110,505 roadway under tectonic stress.</p>
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<p>Comparison of supporting effect of 110,505 roadway before and after taking measures.</p>
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16 pages, 3696 KiB  
Article
Discharge Experiment and Structure Optimisation Simulation of Impulse Sound Source
by Xu Gao, Jing Zhou, Haiming Xie and Xiao Du
Energies 2024, 17(18), 4565; https://doi.org/10.3390/en17184565 - 12 Sep 2024
Abstract
The wave frequency and energy of traditional piezoelectric emission sources used in acoustic logging are limited, which results in an inadequate detection resolution for measuring small-scale geological formations. Additionally, the propagation of these waves in formations is prone to loss and noise interference, [...] Read more.
The wave frequency and energy of traditional piezoelectric emission sources used in acoustic logging are limited, which results in an inadequate detection resolution for measuring small-scale geological formations. Additionally, the propagation of these waves in formations is prone to loss and noise interference, restricting detection to only a few tens of meters around the well. This paper investigates an impulse sound source, a new emission source that can effectively enhance the frequency range and wave energy of traditional sources by generating excitation waves through high-voltage discharges in a fluid-penetrated electrode structure. Firstly, a high-voltage circuit experimental system for the impulse sound source was constructed, and the discharge and response characteristics were experimentally analyzed. Then, four types of needle series electrode structure models were developed to investigate and compare the effects of different electrode structures on the impulse sound source, with the needle-ring electrode demonstrating superior performance. Finally, the needle-ring electrode structure was optimized to develop a ball-tipped needle-ring electrode, which is more suitable for acoustic logging. The results show that the electrode structure directly influences the discharge characteristics of the impulse sound source. After comparison and optimization, the final ball-tipped needle-ring electrode exhibited a broader frequency range—from zero to several hundred thousand Hz—while maintaining a high acoustic amplitude. It has the capability to detect geological areas beyond 100 m and is effective for evaluating micro-fractures and small fracture blocks near wells that require high detection accuracy. This is of significant importance in oil, gas, new energy, and other drilling fields. Full article
(This article belongs to the Section H: Geo-Energy)
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<p>Working circuit diagram of the high-voltage experimental platform for impulse sound source.</p>
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<p>Physical diagram of high-voltage power supply module.</p>
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<p>Needle-bar electrode structure.</p>
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<p>Needle-bar electrode wave generation process: (<b>a</b>) The pre-breakdown stage; (<b>b</b>) the during-breakdown stage; (<b>c</b>) the post-breakdown stage.</p>
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<p>Voltage and current waveforms of needle-bar electrode.</p>
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<p>Pressure–times curve of the shockwave.</p>
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<p>Equivalent circuit diagram of impulse sound source discharge.</p>
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<p>Structural simulation model of the needle-bar electrode.</p>
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<p>(<b>a</b>) Voltage and current waveforms of the needle-bar electrode at the pre-breakdown stage; (<b>b</b>) current waveform of needle-bar electrode in the post-breakdown stage; (<b>c</b>) pressure–time diagram of impulse wave.</p>
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<p>Structural simulation model of the needle-ball electrode.</p>
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<p>Structural simulation model of the needle-needle electrode.</p>
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<p>Structural simulation model of the needle-ring electrode.</p>
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<p>Sound pressure level–frequency plots for needle series electrode structures.</p>
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<p>(<b>a</b>) Ball-tipped needle-ring electrode; (<b>b</b>) partial view of the cone head of the needle electrode.</p>
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<p>Sound pressure level–frequency plots for needle-ring electrode and ball-tipped needle-ring electrode.</p>
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15 pages, 4552 KiB  
Communication
Research on On-Line Monitoring of Grinding Wheel Wear Based on Multi-Sensor Fusion
by Jingsong Duan, Guohua Cao, Guoqing Ma, Zhenglin Yu and Changshun Shao
Sensors 2024, 24(18), 5888; https://doi.org/10.3390/s24185888 - 11 Sep 2024
Abstract
The state of a grinding wheel directly affects the surface quality of the workpiece. The monitoring of grinding wheel wear state can allow one to efficiently identify grinding wheel wear information and to timely and effectively trim the grinding wheel. At present, on-line [...] Read more.
The state of a grinding wheel directly affects the surface quality of the workpiece. The monitoring of grinding wheel wear state can allow one to efficiently identify grinding wheel wear information and to timely and effectively trim the grinding wheel. At present, on-line monitoring technology using specific sensor signals can detect abnormal grinding wheel wear in a timely manner. However, due to the non-linearity and complexity of the grinding wheel wear process, as well as the interference and noise of the sensor signal, the accuracy and reliability of on-line monitoring technology still need to be improved. In this paper, an intelligent monitoring system based on multi-sensor fusion is established, and this system can be used for precise grinding wheel wear monitoring. The proposed system focuses on titanium alloy, a typical difficult-to-process aerospace material, and addresses the issue of low on-line monitoring accuracy found in traditional single-sensor systems. Additionally, a multi-eigenvalue fusion algorithm based on an improved support vector machine (SVM) is proposed. In this study, the mean square value of the wavelet packet decomposition coefficient of the acoustic emission signal, the grinding force ratio of the force signal, and the effective value of the vibration signal were taken as inputs for the improved support vector machine, and the recognition strategy was adjusted using the entropy weight evaluation method. A high-precision grinding machine was used to carry out multiple sets of grinding wheel wear experiments. After being processed by the multi-sensor integrated precision grinding wheel wear intelligent monitoring system, the collected signals can accurately reflect the grinding wheel wear state, and the monitoring accuracy can reach more than 92%. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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<p>KeyenceVXH-200 ultra-depth-of-field microscope.</p>
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<p>Surface morphology of grinding wheel in different wear periods: (<b>a</b>) initial grinding wheel wear; (<b>b</b>) middle grinding wheel wear; (<b>c</b>) late-stage wheel wear.</p>
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<p>Structure of SVM network model for precision grinding wheel wear state identification.</p>
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<p>Experimental setup.</p>
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<p><b>Raw data of acoustic emission signal:</b> (<b>a</b>) Experiment 1-original acoustic emission signal; (<b>b</b>) Experiment 2-original acoustic emission signal; (<b>c</b>) Experiment 3-original acoustic emission signal.</p>
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<p><b>Raw data of acoustic emission signal:</b> (<b>a</b>) Experiment 1-original acoustic emission signal; (<b>b</b>) Experiment 2-original acoustic emission signal; (<b>c</b>) Experiment 3-original acoustic emission signal.</p>
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<p><b>Wavelet packet energy coefficient distribution diagrams:</b> (<b>a</b>) Experiment 1-Wavelet packet energy coefficient distribution diagram ; (<b>b</b>) Experiment 2-Wavelet packet energy coefficient distribution diagram; (<b>c</b>) Experiment 3 Wavelet packet energy coefficient distribution diagram .</p>
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<p>Vibration signal before denoising.</p>
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<p>Vibration signal after denoising signal.</p>
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<p>Chromatogram produced by Leica MAP before the wear of grinding wheel.</p>
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<p>Chromatogram produced by Leica MAP after the wear of the grinding wheel.</p>
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<p>Results of wheel wear status monitoring simulation.</p>
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22 pages, 14713 KiB  
Article
A Proposed Non-Destructive Method Based on Sphere Launching and Piezoelectric Diaphragm
by Cristiano Soares Junior, Paulo Roberto Aguiar, Doriana M. D’Addona, Pedro Oliveira Conceição Junior and Reinaldo Götz Oliveira Junior
Sensors 2024, 24(18), 5874; https://doi.org/10.3390/s24185874 - 10 Sep 2024
Abstract
This work presents the study of a reproducible acoustic emission method based on the launching of a metallic sphere and low-cost piezoelectric diaphragm. For this purpose, tests were first conducted on a carbon fiber-reinforced polymer structure, and then on an aluminum structure for [...] Read more.
This work presents the study of a reproducible acoustic emission method based on the launching of a metallic sphere and low-cost piezoelectric diaphragm. For this purpose, tests were first conducted on a carbon fiber-reinforced polymer structure, and then on an aluminum structure for comparative analysis. The pencil-lead break (PLB) tests were also conducted for comparisons with the proposed method. Different launching heights and elastic deformations of the structures were investigated. The results show higher repeatability for the sphere impact method, as the PLB is more affected by human inaccuracy, and it was also effective in damage detection. Full article
(This article belongs to the Special Issue Feature Papers in Physical Sensors 2024)
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<p>Workbench schematic diagram.</p>
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<p>Test bench. In (<b>a</b>) oscilloscope (1), piezoelectric diaphragm (2), CFRP or aluminum plate (3), damage addition point (4), foam sheet (5), launching device (6), voltage source (7), metal nuts. In (<b>b</b>) (8), metallic sphere. In (<b>c</b>) (9), aluminum template or model (10).</p>
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<p>Plastic deformation analysis due to the metallic sphere impact on CFRP: (<b>a</b>) before; (<b>b</b>) after.</p>
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<p>Plastic deformation study due to the metallic sphere impact on aluminum: (<b>a</b>) 3.9 mm sphere; (<b>b</b>) 6.3 mm sphere.</p>
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<p>The raw signal of repetition 1 from PLB tests on CFRP.</p>
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<p>Average frequency spectra from PLB tests on CFRP.</p>
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<p>Average frequency spectra from PLB tests on aluminum.</p>
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<p>Raw signal from launch tests on CFRP.</p>
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<p>Average frequency spectra from launch tests on CFRP.</p>
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<p>Frequency spectra from launch tests on aluminum.</p>
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<p>Launch tests adding mass to CFRP.</p>
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<p>Launch tests adding mass to aluminum.</p>
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<p>CCDM applied for the tests conducted on CFRP in the frequency band from 1 kHz to 9 kHz.</p>
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<p>CCDM applied for the tests conducted on aluminum in the frequency band from 8 kHz to 16 kHz.</p>
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<p>RMSD applied for the tests conducted on CFRP in the frequency band from 8 to 16 kHz.</p>
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<p>RMSD applied for the tests conducted on aluminum in the frequency band from 8 kHz to 16 kHz.</p>
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<p>PLB tests adding mass to CFRP.</p>
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<p>PLB tests adding mass to aluminum.</p>
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<p>Signal energy for PLB: (<b>a</b>) baseline, (<b>b</b>) damage 1; Launching: baseline (<b>c</b>), (<b>d</b>) damage 1.</p>
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<p>CCDM for CFRP in the frequency band from 20 kHz to 24 kHz.</p>
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<p>RMSD for CFRP in the frequency band from 20 kHz to 24 kHz.</p>
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<p>MSC for CFRP.</p>
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<p>MSC for aluminum.</p>
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23 pages, 13409 KiB  
Article
Estimating Lab-Quake Source Parameters: Spectral Inversion from a Calibrated Acoustic System
by Federico Pignalberi, Giacomo Mastella, Carolina Giorgetti and Marco Maria Scuderi
Sensors 2024, 24(17), 5824; https://doi.org/10.3390/s24175824 - 7 Sep 2024
Abstract
Laboratory acoustic emissions (AEs) serve as small-scale analogues to earthquakes, offering fundamental insights into seismic processes. To ensure accurate physical interpretations of AEs, rigorous calibration of the acoustic system is essential. In this paper, we present an empirical calibration technique that quantifies sensor [...] Read more.
Laboratory acoustic emissions (AEs) serve as small-scale analogues to earthquakes, offering fundamental insights into seismic processes. To ensure accurate physical interpretations of AEs, rigorous calibration of the acoustic system is essential. In this paper, we present an empirical calibration technique that quantifies sensor response, instrumentation effects, and path characteristics into a single entity termed instrument apparatus response. Using a controlled seismic source with different steel balls, we retrieve the instrument apparatus response in the frequency domain under typical experimental conditions for various piezoelectric sensors (PZTs) arranged to simulate a three-component seismic station. Removing these responses from the raw AE spectra allows us to obtain calibrated AE source spectra, which are then effectively used to constrain the seismic AE source parameters. We apply this calibration method to acoustic emissions (AEs) generated during unstable stick-slip behavior of a quartz gouge in double direct shear experiments. The calibrated AEs range in magnitude from −7.1 to −6.4 and exhibit stress drops between 0.075 MPa and 4.29 MPa, consistent with earthquake scaling relation. This result highlights the strong similarities between AEs generated from frictional gouge experiments and natural earthquakes. Through this acoustic emission calibration, we gain physical insights into the seismic sources of laboratory AEs, enhancing our understanding of seismic rupture processes in fault gouge experiments. Full article
(This article belongs to the Section Physical Sensors)
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<p>(<b>a</b>) BRAVA2 biaxial apparatus and calibration setup showing the ball-drop procedure. (<b>b</b>) Rear view of the side blocks showing the piezoelectric sensor positions. (<b>c</b>) AEs from a single ball drop, with an illustration at the top showing the ball trajectory over time. <math display="inline"><semantics> <msub> <mi>T</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>b</mi> </mrow> </msub> </semantics></math> represents the rebound time used to calculate the rebound height (<math display="inline"><semantics> <msub> <mi>h</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>b</mi> </mrow> </msub> </semantics></math>). The inset shows a close-up view of the first AE used for calibration.</p>
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<p>Block diagram showing the physical processes involved in signal modification and the procedure employed to derive the source spectra of AEs by removing the instrument apparatus response. From the top: the convolution (*) of the source function (<math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>) with the instrument apparatus response (<math display="inline"><semantics> <mrow> <mi>i</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>) results in the recorded output signal (<math display="inline"><semantics> <mrow> <mi>s</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>). In the frequency domain, from the output signal (<math display="inline"><semantics> <mrow> <mi>S</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math>) and the theoretical force–time function (<math display="inline"><semantics> <mrow> <mi>F</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math>), the instrument apparatus response function (<math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math>) can be characterized as indicated (red arrows). The source spectrum of an AE can then be obtained from <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>ω</mi> <mo>)</mo> </mrow> </semantics></math> (blue arrows). FFT stands for fast Fourier transform.</p>
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<p>(<b>a</b>) Theoretical spectrum obtained from the FFT of the theoretical force–time function (violet shaded line) for a 7 mm ball diameter, where <math display="inline"><semantics> <msub> <mi mathvariant="normal">Ω</mi> <mn>0</mn> </msub> </semantics></math> is the spectrum amplitude of the flat portion of the spectrum, <math display="inline"><semantics> <msub> <mi>f</mi> <mi>c</mi> </msub> </semantics></math> is the corner frequency, and <span class="html-italic">n</span> is the high-frequency decay. The violet points represent the median value for each bin (see <a href="#sec4dot3-sensors-24-05824" class="html-sec">Section 4.3</a> for the binning procedure). (<b>b</b>) Binned source spectra of the theoretical force–time function for all ball sizes ranging from 0.5 mm to 15 mm.</p>
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<p>Calibration analysis for a ball drop with a 10 mm diameter recorded with the Sh sensor. (<b>a</b>) Windowing procedure for one AE, with the blue line representing the Tuckey taper window and the blue vertical dashed line representing the point where the taper window reaches 1. A zoomed-in view of the first µs is shown in the inset. (<b>b</b>) Acoustic signal after tapering and zero padding of the AE. (<b>c</b>) Acoustic signal after tapering and zero padding of the noise before the AE. (<b>d</b>) Fourier spectrum of the AE. The raw spectrum is shown in black, and the binned spectrum is represented in red. (<b>e</b>) Fourier spectrum of the noise. The raw spectrum is shown in black, and the binned spectrum is indicated in red.</p>
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<p>Raw spectra for five ball drops using a ball with a diameter of 10 mm. The red dashed line indicates the corner frequency of 27.6 kHz derived from Hertzian theory. To retrieve the calibration function, only the portion where <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>&lt;</mo> <msub> <mi>f</mi> <mi>c</mi> </msub> </mrow> </semantics></math> is considered, while <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>&gt;</mo> <msub> <mi>f</mi> <mi>c</mi> </msub> </mrow> </semantics></math> represents the high-frequency decay and is not considered in the calculation of the instrument apparatus response.</p>
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<p>(<b>a</b>) Raw spectra of all ball drops with an SNR &gt; 10 dB. Each line represents the median of the five ball drops performed for each ball. The gray lines represent the noise associated with each spectrum. (<b>b</b>) Spectra corrected according to the <math display="inline"><semantics> <msub> <mi mathvariant="normal">Ω</mi> <mn>0</mn> </msub> </semantics></math> value derived from the theoretical spectra. The instrument apparatus response is represented by the thick black line.</p>
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<p>Instrument apparatus response functions for different sensors at various normal stresses and for both blocks. (<b>a</b>,<b>b</b>) The calibration function for the P sensor at 50 MPa (dark red) and 12 MPa (light red). The slopes indicate the operational mode of the sensor (0 dB/decade, displacement sensor; 20 dB/decade, velocimeter sensor; 40 dB/decade, accelerometer sensor). (<b>c</b>,<b>d</b>) The calibration function for the S<sub>v</sub> sensor at 50 MPa (dark blue) and 12 MPa (light blue). (<b>e</b>,<b>f</b>) The calibration function for the S<sub>h</sub> sensor at 50 MPa (dark green) and 12 MPa (light green). All calibration functions are shown in each plot to facilitate comparison.</p>
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<p>Instrument apparatus response functions for various sensors with and without accounting for the gouge layer in both blocks. Darker lines indicate the instrument apparatus response without considering the gouge layer, while lighter lines represent the response with the gouge layer considered. (<b>a</b>,<b>b</b>) The calibration functions for the P sensor. (<b>c</b>,<b>d</b>) The calibration function for the S<sub>v</sub> sensor. (<b>e</b>,<b>f</b>) The calibration function for the S<sub>h</sub> sensor. All calibration functions are shown in each plot to facilitate comparison.</p>
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<p>Corrected source spectra for each steel ball size with superimposed the theoretical spectra from Hertz theory. The red triangles point to the corner frequency theoretically derived from <math display="inline"><semantics> <mrow> <msub> <mi>f</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <msub> <mi>T</mi> <mi>c</mi> </msub> </mrow> </semantics></math>. It is worth noting the slight variability in the flat spectrum for the 15 mm ball is attributed to minor variations in the impact position resulting from manual dropping.</p>
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<p>Friction curve for the test experiment. The inset on the right shows a zoomed-in view of some seismic cycles. The inset on the left shows the experimental configuration, and the inset on the bottom shows the stress drop of the events as a function of the fault displacement. The red square highlights the events analyzed with our calibration technique to estimate the source parameters.</p>
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<p>Wavelet spectrum of the seismic signal. (<b>a</b>) The evolution of shear stress (black line), normal stress (light blue line), and layer thickness (red line) for the 60 ms surrounding the stress drop. (<b>b</b>) The raw seismic signal from the P sensor. (<b>c</b>) Wavelet spectrogram of the raw acoustic signal shown in (<b>b</b>). (<b>d</b>) The high-pass-filtered waveform at 10 kHz. (<b>e</b>) Wavelet spectrogram of the high-pass-filtered acoustic signal shown in (<b>d</b>).</p>
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<p>Waveforms and spectra of the same AE recorded with different sensors. The left column refers to the P sensor, the central column to the S<sub>v</sub> sensor, and the right column to the S<sub>h</sub> sensor. (<b>a</b>–<b>c</b>) Raw waveforms. (<b>d</b>–<b>f</b>) High-pass-filtered waveforms at 10 kHz with a zoomed-in view of the AE in the lower right. (<b>g</b>–<b>i</b>) The instrument apparatus response (red line) with the AE spectrum (blue line). (<b>j</b>–<b>l</b>) The source spectrum derived from the AE spectrum and the instrument apparatus response. The gray line represents the Brune fit, and the red triangle indicates the corner frequency.</p>
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<p>Source parameters estimated with different sensors (P in red, S<sub>v</sub> in blue, and S<sub>h</sub> in green). Error bars represent two standard deviations.</p>
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27 pages, 12379 KiB  
Article
Experimental and Numerical Investigation of Acoustic Emission Source Localization Using an Enhanced Guided Wave Phased Array Method
by Jiaying Sun, Zexing Yu, Chao Xu and Fei Du
Sensors 2024, 24(17), 5806; https://doi.org/10.3390/s24175806 - 6 Sep 2024
Abstract
To detect damage in mechanical structures, acoustic emission (AE) inspection is considered as a powerful tool. Generally, the classical acoustic emission detection method uses a sparse sensor array to identify damage and its location. It often depends on a pre-defined wave velocity and [...] Read more.
To detect damage in mechanical structures, acoustic emission (AE) inspection is considered as a powerful tool. Generally, the classical acoustic emission detection method uses a sparse sensor array to identify damage and its location. It often depends on a pre-defined wave velocity and it is difficult to yield a high localization accuracy for complicated structures using this method. In this paper, the passive guided wave phased array method, a dense sensor array method, is studied, aiming to obtain better AE localization accuracy in aluminum thin plates. Specifically, the proposed method uses a cross-shaped phased array enhanced with four additional far-end sensors for AE source localization. The proposed two-step method first calculates the real-time velocity and the polar angle of the AE source using the phased array algorithm, and then solves the location of the AE source with the additional far-end sensor. Both numerical and physical experiments on an aluminum flat panel are carried out to validate the proposed method. It is found that using the cross-shaped guided wave phased array method with enhanced far-end sensors can localize the coordinates of the AE source accurately without knowing the wave velocity in advance. The proposed method is also extended to a stiffened thin-walled structure with high localization accuracy, which validates its AE source localization ability for complicated structures. Finally, the influences of cross-shaped phased array element number and the time window length on the proposed method are discussed in detail. Full article
(This article belongs to the Special Issue Recent Advances in Structural Health Monitoring and Damage Detection)
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Figure 1
<p>Layout of the enhanced phased array.</p>
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<p>Illustration of wave velocity calculation.</p>
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<p>Flowchart of the iterative process to solve AE source polar angle.</p>
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<p>Method of location determination.</p>
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<p>Flowchart of AE source location determination.</p>
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<p>The location of sensors and AE sources in aluminum plate.</p>
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<p>Simulated AE source function.</p>
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<p>AE signal of ID 3 in the simulated calculation.</p>
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<p>The AE signals of wavelet coefficients after CWT at frequency 200 kHz (simulated validation).</p>
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<p>Superimposed signals in identified polar angle and other angles (simulated validation).</p>
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<p>The shifted signals of wavelet coefficients at angle <math display="inline"><semantics> <mrow> <mn>66.1</mn> <mo>°</mo> </mrow> </semantics></math> (simulated validation).</p>
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<p>The detection result of AE source ID 3 (simulated validation).</p>
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<p>Localization results for different AE events (simulated validation).</p>
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<p>Experimental setup of the enhanced phased array method.</p>
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<p>AE signal of ID3 in experiment.</p>
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<p>The AE signals of wavelet coefficients after CWT at frequency 200 kHz (experimental validation).</p>
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<p>Superimposed signals in identified polar angle and other angles (experimental validation).</p>
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<p>The shifted signals of wavelet coefficients at angle <math display="inline"><semantics> <mrow> <mn>67.9</mn> <mo>°</mo> </mrow> </semantics></math> (experimental validation).</p>
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<p>The detection result of the AE sources ID 3 (experimental validation).</p>
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<p>Initial wave velocity convergence analysis in experimental event ID 3.</p>
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<p>Localization results for different AE events (experimental validation).</p>
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<p>The location of sensors and the AE sources in the triangulation technique.</p>
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<p>The comparison of localization results between the triangulation method and the enhanced phased array method.</p>
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<p>The overview of the stiffened plate.</p>
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<p>The AE source localization results of the stiffened plate.</p>
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<p>Configuration of different element numbers.</p>
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<p>The comparison of localization results among 3-element array, 5-element array, and 7-element array.</p>
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<p>The schematic diagram of different time window lengths.</p>
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<p>The results of localizing AE sources under different time window lengths.</p>
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23 pages, 17032 KiB  
Article
Experimental Investigation of Rotor Noise in Reverse Non-Axial Inflow
by Liam Hanson, Leone Trascinelli, Bin Zang and Mahdi Azarpeyvand
Aerospace 2024, 11(9), 730; https://doi.org/10.3390/aerospace11090730 - 6 Sep 2024
Abstract
This paper experimentally characterises the far-field noise emissions of a rotor operating in reverse non-axial inflow conditions. Specifically, experiments were undertaken at a range of rotor tilting angles and inflow velocities to investigate the effects of negative tilting on rotor acoustics and their [...] Read more.
This paper experimentally characterises the far-field noise emissions of a rotor operating in reverse non-axial inflow conditions. Specifically, experiments were undertaken at a range of rotor tilting angles and inflow velocities to investigate the effects of negative tilting on rotor acoustics and their correlation with aerodynamic performance. The results show that the forces and moments experienced by the rotor blades change significantly with increasing inflow velocity and increasing negative tilting angle. Correspondingly, distinct modifications to the far-field acoustic spectra are observed for the negatively tilted rotor when compared to the edgewise condition, with the broadband noise content notably increasing. Moreover, for a given tilting angle, the broadband noise component is accentuated with increasing inflow velocity, similar to when the negative tilting angle is increased. With reference to the flow-field surveys conducted in the literature and a preliminary in-house flow measurement, the increase in broadband content can possibly be attributed to the heightened level of ingestion of blade self-turbulence, i.e., the ingestion of turbulent wake generated by the upstream portion of the rotor by the downstream portion. At lower inflow velocities, the magnitude of the blade passing frequency at each of the observer angles is found to change minimally with negative tilt. In contrast, at higher inflow velocities, the directivity pattern and intensity of both the blade passing frequency and the overall sound pressure level are shown to change with increases in magnitude, particularly at downstream observer locations with negative tilt. These findings have important ramifications for the design and suitable operational profile of aerial vehicles for future urban air mobility applications. Full article
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Figure 1
<p>Schematic showing an eVTOL flight path in an urban environment. Reverse non-axial inflow conditions are likely to be experienced by eVTOL rotors during landing transition maneuvers. The asterisk indicates the flight conditions being investigated in the current paper.</p>
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<p>Details of the rotor assembly showing (<b>a</b>) the definition of tilting angle (<math display="inline"><semantics> <mi>α</mi> </semantics></math>) and coordinate system and (<b>b</b>) the different components annotated on the test rig.</p>
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<p>Chord length and pitch angle distribution of the 12″ × 6″ rotor used in the present study.</p>
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<p>Schematic representation of the experimental setup in the wind tunnel showing (<b>a</b>) the side-view of the setup with top polar microphone arc and (<b>b</b>) the back-view of the setup with the distance-corrected polar side array.</p>
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<p>Interpretation of the flow field of the rotor at a negative tilting orientation for (<b>a</b>) low inflow velocity and (<b>b</b>) high inflow velocity based on previous findings [<a href="#B18-aerospace-11-00730" class="html-bibr">18</a>,<a href="#B21-aerospace-11-00730" class="html-bibr">21</a>] and an in-house PIV experiment [<a href="#B23-aerospace-11-00730" class="html-bibr">23</a>].</p>
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<p>Time-averaged aerodynamic coefficients for a rotor operating at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> </mrow> </semantics></math> RPM presented as a function of the advance ratio (<math display="inline"><semantics> <mi>μ</mi> </semantics></math>) at different tilting angles. The following coefficients are presented: mean thrust coefficient (<math display="inline"><semantics> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">T</mi> </msub> </semantics></math>) variation (<b>a</b>), mean power coefficient (<math display="inline"><semantics> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">P</mi> </msub> </semantics></math>) variation (<b>b</b>), mean yaw force coefficient (<math display="inline"><semantics> <msub> <mi mathvariant="normal">C</mi> <mi>Fy</mi> </msub> </semantics></math>) variation (<b>c</b>) and mean yawing moment coefficient (<math display="inline"><semantics> <msub> <mi mathvariant="normal">C</mi> <mi>My</mi> </msub> </semantics></math>) variation (<b>d</b>).</p>
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<p>Sound pressure level spectra of a rotor operating at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> measured from three observer locations of <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <msup> <mn>60</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <msup> <mn>90</mn> <mo>∘</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>120</mn> <mo>∘</mo> </msup> </semantics></math> at inflow velocities of (<b>a</b>–<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">U</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>d</b>–<b>f</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>g</b>–<b>i</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>j</b>–<b>l</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles from <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>. The blue and red vertical lines in each sub-figure indicate both the rotor shaft tones (<math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mn>1.5</mn> </mrow> </semantics></math>) and blade passing frequency tones (<span class="html-italic">m</span> = 1–3) respectively. The grey, red and blue shaded regions in (<b>c</b>) indicate three frequency bands: LF (<math display="inline"><semantics> <mrow> <mn>160</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> <mo>≤</mo> <mi>f</mi> <mo>&lt;</mo> <mn>3</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math>), MF (<math display="inline"><semantics> <mrow> <mn>3</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> <mo>≤</mo> <mi>f</mi> <mo>&lt;</mo> <mn>10</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math>) and HF (<math display="inline"><semantics> <mrow> <mi>f</mi> <mo>≥</mo> <mn>10</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math>).</p>
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<p>Sound pressure level spectra of a rotor operating at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> measured from three observer locations of <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>=</mo> <msup> <mn>74</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <msup> <mn>90</mn> <mo>∘</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>107</mn> <mo>∘</mo> </msup> </semantics></math> at inflow velocities of (<b>a</b>–<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">U</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>d</b>–<b>f</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>g</b>–<b>i</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>j</b>–<b>l</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles from <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>. The blue and red vertical lines in each sub-figure indicate both the rotor shaft tones (<span class="html-italic">m</span> = 0.5, 1.5) and blade passing frequency tones (<span class="html-italic">m</span> = 1–3) respectively. The grey, red and blue shaded regions in (<b>c</b>) indicate three frequency bands: LF (160 Hz ≤ <span class="html-italic">f</span> &lt; 3 kHz), MF (3 kHz ≤ <span class="html-italic">f</span> &lt; 10 kHz) and HF ( <span class="html-italic">f</span> ≥ 10 kHz).</p>
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<p>Far- field noise directivity pattern at the fundamental BPF (<math display="inline"><semantics> <msub> <mi>SPL</mi> <mrow> <mi mathvariant="normal">m</mi> <mo>=</mo> <mn>1</mn> </mrow> </msub> </semantics></math>) on the top array (<math display="inline"><semantics> <mi>θ</mi> </semantics></math>) at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> for inflow velocities of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">U</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles of <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Far- field noise directivity pattern at the fundamental BPF (<math display="inline"><semantics> <msub> <mi>SPL</mi> <mrow> <mi mathvariant="normal">m</mi> <mo>=</mo> <mn>1</mn> </mrow> </msub> </semantics></math>) on the side array (<math display="inline"><semantics> <mi>ϕ</mi> </semantics></math>) at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> for inflow velocities of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">U</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> over tilting angles of <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Overall sound pressure level and directivity pattern of the rotor on the top array (<math display="inline"><semantics> <mi>θ</mi> </semantics></math>) at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> for inflow velocities of (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles of <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Overall sound pressure level and directivity pattern of a rotor on the side array (<math display="inline"><semantics> <mi>ϕ</mi> </semantics></math>) at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> for inflow velocities of (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles of <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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