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19 pages, 5357 KiB  
Article
Planetary Gearboxes Fault Diagnosis Based on Markov Transition Fields and SE-ResNet
by Yanyan Liu, Tongxin Gao, Wenxu Wu and Yongquan Sun
Sensors 2024, 24(23), 7540; https://doi.org/10.3390/s24237540 - 26 Nov 2024
Cited by 1 | Viewed by 492
Abstract
The working conditions of planetary gearboxes are complex, and their structural couplings are strong, leading to low reliability. Traditional deep neural networks often struggle with feature learning in noisy environments, and their reliance on one-dimensional signals as input fails to capture the interrelationships [...] Read more.
The working conditions of planetary gearboxes are complex, and their structural couplings are strong, leading to low reliability. Traditional deep neural networks often struggle with feature learning in noisy environments, and their reliance on one-dimensional signals as input fails to capture the interrelationships between data points. To address these challenges, we proposed a fault diagnosis method for planetary gearboxes that integrates Markov transition fields (MTFs) and a residual attention mechanism. The MTF was employed to encode one-dimensional signals into feature maps, which were then fed into a residual networks (ResNet) architecture. To enhance the network’s ability to focus on important features, we embedded the squeeze-and-excitation (SE) channel attention mechanism into the ResNet34 network, creating a SE-ResNet model. This model was trained to effectively extract and classify features. The developed method was validated using a specific dataset and achieved an accuracy of about 98.1%. The results demonstrate the effectiveness and reliability of the developed method in diagnosing faults in planetary gearboxes under strong noise conditions. Full article
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<p>Diagram of fault diagnosis process.</p>
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<p>Convolution process.</p>
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<p>Residual block.</p>
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<p>Residual network structure.</p>
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<p>Residual attention module.</p>
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<p>MTF-SE-ResNet model.</p>
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<p>Schematic diagram of the full connectivity layer.</p>
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<p>Composition of the test bench and arrangement of measurement points.</p>
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<p>Planetary gearbox fault forms.</p>
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<p>Data segmentation chart.</p>
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<p>Logical block diagrams of the MTF-ResNet algorithm.</p>
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<p>Comparison of original and downsampled signal spectra.</p>
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<p>MTF-ResNet confusion matrix with ROC curves.</p>
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<p>Heat map of the nodes of the residual network of solar wheel failures. (<b>a</b>) represents the output heatmap of the first Residual Block, (<b>b</b>) represents the output heatmap of the second Residual Block, (<b>c</b>) represents the output heatmap of the third Residual Block, and (<b>d</b>) represents the output heatmap of the fourth Residual Block.</p>
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<p>T-SNE visualization of feature dimensionality reduction.</p>
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<p>Fault classification accuracy analysis results for 10 tests on planetary gearboxes.orange stripes representing CNN accuracy, green for MTF-CNN, purple for ResNet34, and yellow for the method proposed in this paper.</p>
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20 pages, 17284 KiB  
Article
Fault-Line Selection Method in Active Distribution Networks Based on Improved Multivariate Variational Mode Decomposition and Lightweight YOLOv10 Network
by Sizu Hou and Wenyao Wang
Energies 2024, 17(19), 4958; https://doi.org/10.3390/en17194958 - 3 Oct 2024
Viewed by 1161
Abstract
In active distribution networks (ADNs), the extensive deployment of distributed generations (DGs) heightens system nonlinearity and non-stationarity, which can weaken fault characteristics and reduce fault detection accuracy. To improve fault detection accuracy in distribution networks, a method combining improved multivariate variational mode decomposition [...] Read more.
In active distribution networks (ADNs), the extensive deployment of distributed generations (DGs) heightens system nonlinearity and non-stationarity, which can weaken fault characteristics and reduce fault detection accuracy. To improve fault detection accuracy in distribution networks, a method combining improved multivariate variational mode decomposition (IMVMD) and YOLOv10 network for active distribution network fault detection is proposed. Firstly, an MVMD method optimized by the northern goshawk optimization (NGO) algorithm named IMVMD is introduced to adaptively decompose zero-sequence currents at both ends of line sources and loads into intrinsic mode functions (IMFs). Secondly, considering the spatio-temporal correlation between line sources and loads, a dynamic time warping (DTW) algorithm is utilized to determine the optimal alignment path time series for corresponding IMFs at both ends. Then, the Markov transition field (MTF) transforms the 1D time series into 2D spatio-temporal images, and the MTF images of all lines are concatenated to obtain a comprehensive spatio-temporal feature map of the distribution network. Finally, using the spatio-temporal feature map as input, the lightweight YOLOv10 network autonomously extracts fault features to achieve precise fault-line selection. Experimental results demonstrate the robustness of the proposed method, achieving a fault detection accuracy of 99.88%, which can ensure accurate fault-line selection under complex scenarios involving simultaneous phase-to-ground faults at two points. Full article
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<p>Current distribution diagram of single-phase grounding fault of neutral ungrounded system with DG. (<b>a</b>) DG is connected downstream of the ground fault location; (<b>b</b>) DG is connected upstream of the ground fault location.</p>
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<p>Algorithm flowchart of IMVMD.</p>
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<p>The original simulation signal.</p>
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<p>EMD decomposition results.</p>
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<p>IMVMD decomposition results.</p>
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<p>MTF image generation process.</p>
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<p>Lightweight YOLOv10 network structure.</p>
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<p>Flow chart of fault-line selection.</p>
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<p>Active distribution network topology.</p>
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<p>Lightweight YOLOv10 training results.</p>
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<p>Confusion matrix fault-line selection results.</p>
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<p>Fault-line selection result for high-resistance grounding fault.</p>
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<p>Fault-line selection result after increasing the number of DGs.</p>
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<p>Dynamic simulation fault diagnosis experimental platform.</p>
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<p>Simulation topology model.</p>
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16 pages, 6475 KiB  
Article
Exploring Inner Speech Recognition via Cross-Perception Approach in EEG and fMRI
by Jiahao Qin, Lu Zong and Feng Liu
Appl. Sci. 2024, 14(17), 7720; https://doi.org/10.3390/app14177720 - 1 Sep 2024
Cited by 1 | Viewed by 1959
Abstract
Multimodal brain signal analysis has shown great potential in decoding complex cognitive processes, particularly in the challenging task of inner speech recognition. This paper introduces an innovative I nner Speech Recognition via Cross-Perception (ISRCP) approach that significantly enhances accuracy by fusing electroencephalography (EEG) [...] Read more.
Multimodal brain signal analysis has shown great potential in decoding complex cognitive processes, particularly in the challenging task of inner speech recognition. This paper introduces an innovative I nner Speech Recognition via Cross-Perception (ISRCP) approach that significantly enhances accuracy by fusing electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data. Our approach comprises three core components: (1) multigranularity encoders that separately process EEG time series, EEG Markov Transition Fields, and fMRI spatial data; (2) a cross-perception expert structure that learns both modality-specific and shared representations; and (3) an attention-based adaptive fusion strategy that dynamically adjusts the contributions of different modalities based on task relevance. Extensive experiments on the Bimodal Dataset on Inner Speech demonstrate that our model outperforms existing methods across accuracy and F1 score. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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<p>Inner speech using EEG and FMRI data.</p>
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<p>The process of transforming EEG signals into MTF images.</p>
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<p>Visualization of EEG data for 8 classes.</p>
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<p>Visualization of EEG data for 2 classes.</p>
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<p>Visualization of fMRI data for 8 classes.</p>
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<p>Visualization of fMRI data for 2 classes.</p>
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24 pages, 2042 KiB  
Article
A Cross-Working Condition-Bearing Diagnosis Method Based on Image Fusion and a Residual Network Incorporating the Kolmogorov–Arnold Representation Theorem
by Ziyi Tang, Xinhao Hou, Xin Wang and Jifeng Zou
Appl. Sci. 2024, 14(16), 7254; https://doi.org/10.3390/app14167254 - 17 Aug 2024
Viewed by 1277
Abstract
With the optimization and advancement of industrial production and manufacturing, the application scenarios of bearings have become increasingly diverse and highly coupled. This complexity poses significant challenges for the extraction of bearing fault features, consequently affecting the accuracy of cross-condition fault diagnosis methods. [...] Read more.
With the optimization and advancement of industrial production and manufacturing, the application scenarios of bearings have become increasingly diverse and highly coupled. This complexity poses significant challenges for the extraction of bearing fault features, consequently affecting the accuracy of cross-condition fault diagnosis methods. To improve the extraction and recognition of fault features and enhance the diagnostic accuracy of models across different conditions, this paper proposes a cross-condition bearing diagnosis method. This method, named MCR-KAResNet-TLDAF, is based on image fusion and a residual network that incorporates the Kolmogorov–Arnold representation theorem. Firstly, the one-dimensional vibration signals of the bearing are processed using Markov transition field (MTF), continuous wavelet transform (CWT), and recurrence plot (RP) methods, converting the resulting images to grayscale. These grayscale images are then multiplied by corresponding coefficients and fed into the R, G, and B channels for image fusion. Subsequently, fault features are extracted using a residual network enhanced by the Kolmogorov–Arnold representation theorem. Additionally, a domain adaptation algorithm combining multiple kernel maximum mean discrepancy (MK-MMD) and conditional domain adversarial network with entropy conditioning (CDAN+E) is employed to align the source and target domains, thereby enhancing the model’s cross-condition diagnostic accuracy. The proposed method was experimentally validated on the Case Western Reserve University (CWRU) dataset and the Jiangnan University (JUN) dataset, which include the 6205-2RS JEM SKF, N205, and NU205 bearing models. The method achieved accuracy rates of 99.36% and 99.889% on the two datasets, respectively. Comparative experiments from various perspectives further confirm the superiority and effectiveness of the proposed model. Full article
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<p>Domain adaptation.</p>
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<p>The proposed MCR-KAResNet-TLDAF framework.</p>
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<p>MCR image fusion process.</p>
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<p>KAResNet framework.</p>
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<p>Principles of domain adaptation algorithms incorporating MK-MMD and CDAN+E.</p>
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<p>CWRU dataset experimental platform.</p>
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<p>Time series waveforms of CWRU dataset bearings under different health conditions.</p>
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<p>Results of the image fusion experiments on the CWRU dataset: (<b>a</b>) first group; (<b>b</b>) second group; (<b>c</b>) third group.</p>
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<p>The average accuracy of different domain adaptation algorithms on the CWRU dataset.</p>
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<p>Average accuracy of fault diagnosis for different models on the CWRU dataset.</p>
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<p>JNU dataset experimental platform.</p>
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<p>Time series waveforms of CWRU dataset bearings under different health conditions.</p>
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<p>Results of the image fusion experiments on the JNU dataset: (<b>a</b>) first group; (<b>b</b>) second group; (<b>c</b>) third group.</p>
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<p>Average accuracy of different domain adaptation algorithms on the JNU dataset.</p>
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<p>Average accuracy of fault diagnosis for different models on the JNU dataset.</p>
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12 pages, 1657 KiB  
Article
Developing Theoretical Models for Atherosclerotic Lesions: A Methodological Approach Using Interdisciplinary Insights
by Amun G. Hofmann
Life 2024, 14(8), 979; https://doi.org/10.3390/life14080979 - 5 Aug 2024
Viewed by 856
Abstract
Atherosclerosis, a leading cause of cardiovascular disease, necessitates advanced and innovative modeling techniques to better understand and predict plaque dynamics. The present work presents two distinct hypothetical models inspired by different research fields: the logistic map from chaos theory and Markov models from [...] Read more.
Atherosclerosis, a leading cause of cardiovascular disease, necessitates advanced and innovative modeling techniques to better understand and predict plaque dynamics. The present work presents two distinct hypothetical models inspired by different research fields: the logistic map from chaos theory and Markov models from stochastic processes. The logistic map effectively models the nonlinear progression and sudden changes in plaque stability, reflecting the chaotic nature of atherosclerotic events. In contrast, Markov models, including traditional Markov chains, spatial Markov models, and Markov random fields, provide a probabilistic framework to assess plaque stability and transitions. Spatial Markov models, visualized through heatmaps, highlight the spatial distribution of transition probabilities, emphasizing local interactions and dependencies. Markov random fields incorporate complex spatial interactions, inspired by advances in physics and computational biology, but present challenges in parameter estimation and computational complexity. While these hypothetical models offer promising insights, they require rigorous validation with real-world data to confirm their accuracy and applicability. This study underscores the importance of interdisciplinary approaches in developing theoretical models for atherosclerotic plaques. Full article
(This article belongs to the Special Issue Microvascular Dynamics: Insights and Applications)
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<p>Examples of the behavior of the logistic map for different values of <span class="html-italic">r</span> – 1.8 (<b>A</b>), 2.8 (<b>B</b>), and 3.8 (<b>C</b>). (<span class="html-italic">t</span><sub>0</sub> = 0.1).</p>
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<p>Hypothetic models of a stable, asymptomatic plaque (<b>A</b>) and an unstable, potentially symptomatic plaque (<b>B</b>). A–C refer to corresponding plaque illustrations in <a href="#life-14-00979-f003" class="html-fig">Figure 3</a>. Parameter <span class="html-italic">r</span> increases in both examples, by a constant factor for each generation (0.05 in (<b>A</b>) vs. 0.08 in (<b>B</b>)). The red line in (<b>B</b>) marks the beginning of the oscillatory phase that reflects a disease stage where patients are at risk of cardiovascular events due to unstable plaques.</p>
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<p>Different disease stages of an atherosclerotic plaque. (<b>A</b>) Depicts an early lesion with minimal luminal reduction, (<b>B</b>) a further developed but asymptomatic manifestation, and (<b>C</b>) an unstable plaque that is characterized by progressed luminal reduction, rupture, and subsequent thrombosis (Created with <a href="http://BioRender.com" target="_blank">BioRender.com</a>).</p>
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<p><a href="#life-14-00979-f004" class="html-fig">Figure 4</a> illustrates, for a given value of <span class="html-italic">P<sub>t</sub></span> in the logistic map, the proportion of values of <span class="html-italic">r</span> resulting in a subsequent decrease in <span class="html-italic">P</span><sub><span class="html-italic">t</span>+1</sub>. As <span class="html-italic">P</span> increases, the proportion of potential values of <span class="html-italic">r</span> (under the boundaries of 0 and 3.5, where the function always exhibits chaotic behavior) leading to a decrease in <span class="html-italic">P</span> in the subsequent generation increases approximately exponentially. This corresponds to the observation that bigger atherosclerotic plaques are more likely to cause cardiovascular events.</p>
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<p><a href="#life-14-00979-f005" class="html-fig">Figure 5</a> illustrates how spatial Markov models can be used to assemble heatmaps visualizing the probability of a plaque area to become unstable and thereby more likely to cause symptomatic events. A three-dimensional plaque can be visualized in a two-dimensional heatmap analogous to the flattened plaque surface (red indicating higher probability, blue lower probability).</p>
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19 pages, 28563 KiB  
Article
Intelligent Fault Diagnosis of Rolling Bearings Based on Markov Transition Field and Mixed Attention Residual Network
by Anshi Tong, Jun Zhang, Danfeng Wang and Liyang Xie
Appl. Sci. 2024, 14(12), 5110; https://doi.org/10.3390/app14125110 - 12 Jun 2024
Cited by 1 | Viewed by 1009
Abstract
To address the problems of existing methods that struggle to effectively extract fault features and unstable model training using unbalanced data, this paper proposes a new fault diagnosis method for rolling bearings based on a Markov Transition Field (MTF) and Mixed Attention Residual [...] Read more.
To address the problems of existing methods that struggle to effectively extract fault features and unstable model training using unbalanced data, this paper proposes a new fault diagnosis method for rolling bearings based on a Markov Transition Field (MTF) and Mixed Attention Residual Network (MARN). The acquired vibration signals are transformed into two-dimensional MTF feature images as network inputs to avoid the loss of the original signal information, while retaining the temporal correlation; then, the mixed attention mechanism is inserted into the residual structure to enhance the feature extraction capability, and finally, the network is trained and outputs diagnostic results. In order to validate the feasibility of the MARN, other popular deep learning (DL) methods are compared on balanced and unbalanced datasets divided by a CWRU fault bearing dataset, and the proposed method results in superior performance. Ultimately, the proposed method achieves an average recognition accuracy of 99.5% and 99.2% under the two categories of divided datasets, respectively. Full article
(This article belongs to the Collection Bearing Fault Detection and Diagnosis)
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<p>MTF encoding.</p>
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<p>Residual structure.</p>
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<p>Channel attention mechanism for MARN (CA, compressing and splitting the feature matrices to obtain the channel attention matrixes).</p>
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<p>Spatial attention mechanism for MARN (SA, pooling operation followed by dimensionality reduction to get the spatial feature matrixes).</p>
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<p>MARN model structure (residual structure and mixed attention mechanisms composed with fault classification by Softmax).</p>
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<p>Fault diagnosis process (Steps 1–3 are data preprocessing, model training, and deriving diagnostic results, respectively).</p>
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<p>CWRU bearing experiment platform [<a href="#B22-applsci-14-05110" class="html-bibr">22</a>].</p>
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<p>Data enhancement.</p>
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<p>MTF coded images. (<b>a</b>) NOR-L<sub>0</sub>; (<b>b</b>) IR-L<sub>1</sub>; (<b>c</b>) IR-L<sub>2</sub>; (<b>d</b>) IR-L<sub>3</sub>; (<b>e</b>) RF-L<sub>4</sub>; (<b>f</b>) RF-L<sub>5</sub>; (<b>g</b>) RF-L<sub>6</sub>; (<b>h</b>) OR-L<sub>7</sub>; (<b>i</b>) OR-L<sub>8</sub>; (<b>j</b>) OR-L<sub>9</sub>.</p>
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<p>Example images of different 2D transformation methods: (<b>a</b>) MTF; (<b>b</b>) GADF; (<b>c</b>) GASF; (<b>d</b>) RP.</p>
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<p>Training curves for different transformation methods: (<b>a</b>) Validation accuracy; (<b>b</b>) Training loss.</p>
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<p>Training curves for different attention mechanisms: (<b>a</b>) Validation accuracy; (<b>b</b>) training loss.</p>
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<p>Confusion matrices: (<b>a</b>) D<sub>A</sub>; (<b>b</b>) D<sub>B</sub>; (<b>c</b>) D<sub>C</sub>; (<b>d</b>) D<sub>D</sub>.</p>
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<p>t-SNE dimensionality reduction: (<b>a</b>) D<sub>A</sub>; (<b>b</b>) D<sub>B</sub>; (<b>c</b>) D<sub>C</sub>; (<b>d</b>) D<sub>D</sub>.</p>
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<p>Training performance curves comparing different models: (<b>a</b>) D<sub>A</sub> validation accuracy; (<b>b</b>) D<sub>A</sub> training loss; (<b>c</b>) D<sub>B</sub> validation accuracy; (<b>d</b>) D<sub>B</sub> training loss.</p>
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<p>Confusion matrices comparing different methods. (From (<b>a</b>–<b>e</b>) for FcaNet/SE-ResNet/ResNet50/NCNN/MobileNet-v3, and from (<b>1</b>–<b>4</b>) for D<sub>A</sub>–D<sub>D</sub>, respectively).</p>
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<p>Comparison of different methods for t-SNE (from (<b>a</b>–<b>e</b>) for FcaNet/SE-ResNet/ResNet50/NCNN/MobileNet-v3, and from (<b>1</b>–<b>4</b>) for D<sub>A</sub>–D<sub>D</sub>, respectively).</p>
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20 pages, 16972 KiB  
Article
Sideband Vibro-Acoustics Suppression and Numerical Prediction of Permanent Magnet Synchronous Motor Based on Markov Chain Random Carrier Frequency Modulation
by Yong Chen, Bingxiao Yan, Liming Zhang, Kefu Yao and Xue Jiang
Appl. Sci. 2024, 14(11), 4808; https://doi.org/10.3390/app14114808 - 2 Jun 2024
Cited by 1 | Viewed by 725
Abstract
This paper presents a Markov chain random carrier frequency modulation (MRCFM) technique for suppressing sideband vibro-acoustic responses caused by discontinuous pulse-width modulation (DPWM) in permanent magnet synchronous motors (PMSMs) for new energy vehicles. Firstly, the spectral and order distributions of the sideband current [...] Read more.
This paper presents a Markov chain random carrier frequency modulation (MRCFM) technique for suppressing sideband vibro-acoustic responses caused by discontinuous pulse-width modulation (DPWM) in permanent magnet synchronous motors (PMSMs) for new energy vehicles. Firstly, the spectral and order distributions of the sideband current harmonics and radial electromagnetic forces introduced by DPWM are characterized and identified. Then, the principle and implementation method of three-state Markov chain random number generation are proposed, and particle swarm optimization (PSO) algorithm is chosen to quickly find the key parameters of transition probability and random gain. A Simulink and JMAG multi-physics field co-simulation model is built to simulate and predict the suppression effect of the MRCFM method on the sideband vibro-acoustic response. Finally, a 12-slot-10-pole PMSM test platform is built for experimental testing. The results show that the sideband current harmonics and vibro-acoustic response are effectively suppressed after the optimization of Markov chain algorithm. The constructed multi-physics field co-simulation model can accurately predict the amplitude characteristics of the sideband current harmonics and vibro-acoustic response. Full article
(This article belongs to the Section Acoustics and Vibrations)
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<p>Diagram of the voltage space vector.</p>
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<p>DPWM switching sequence in sector I.</p>
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<p>Schematic diagram of random PWM.</p>
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<p>The simulation results of the carrier frequency in conventional RCFM.</p>
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<p>State parameter transition diagram of three-state Markov chain carrier frequency.</p>
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<p>The random carrier frequency results with three-state Markov chain.</p>
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<p>Flowchart of particle swarm optimization.</p>
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<p>Results of randomized parameters with PSO algorithm: (<b>a</b>) The error of the objective function; (<b>b</b>) The value of the transfer probability; (<b>c</b>) The value of the random gain.</p>
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<p>Simulation prediction of sideband current harmonics under different PWM strategies: (<b>a</b>) DPWMMIN and DPWMMAX; (<b>b</b>) DPWM0 and DPWM2; (<b>c</b>) DPWM1 and DPWM3.</p>
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<p>Prediction of the suppression effect of Markov chain random carrier frequency modulation on sideband current harmonics of different PWM strategies: (<b>a</b>) DPWMMIN and DPWMMAX; (<b>b</b>) DPWM0 and DPWM2; (<b>c</b>) DPWM1 and DPWM3.</p>
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<p>The multi-physics field analysis process for electromagnetic noise of PMSM.</p>
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<p>Simulation prediction of sideband vibration response under different PWM strategies: (<b>a</b>) DPWMMIN and DPWMMAX; (<b>b</b>) DPWM0 and DPWM2; (<b>c</b>) DPWM1 and DPWM3.</p>
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<p>Prediction of the suppression effect of Markov chain random carrier frequency modulation on sideband vibration response of different PWM strategies: (<b>a</b>) DPWMMIN and DPWMMAX; (<b>b</b>) DPWM0 and DPWM2; (<b>c</b>) DPWM1 and DPWM3.</p>
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<p>Simulation prediction of sideband acoustic response under different PWM strategies: (<b>a</b>) DPWMMIN and DPWMMAX; (<b>b</b>) DPWM0 and DPWM2; (<b>c</b>) DPWM1 and DPWM3.</p>
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<p>Prediction of the suppression effect of Markov chain random carrier frequency modulation on sideband acoustic response of different PWM strategies: (<b>a</b>) DPWMMIN and DPWMMAX; (<b>b</b>) DPWM0 and DPWM2; (<b>c</b>) DPWM1 and DPWM3.</p>
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<p>The PMSM vibration noise test system.</p>
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<p>Experimental comparison of sideband current harmonics before and after MRCFM optimization: (<b>a</b>) Fixed carrier frequency modulation; (<b>b</b>) Markov chain random carrier frequency modulation.</p>
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<p>Comparison of simulated and measured harmonic peaks of sideband currents with different modulation strategies.</p>
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<p>Experimental comparison of sideband vibration response before and after MRCFM optimization: (<b>a</b>) Fixed carrier frequency modulation; (<b>b</b>) Markov chain random carrier frequency modulation.</p>
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<p>Comparison of simulated and measured peak sideband vibration response with different modulation strategies.</p>
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<p>Experimental comparison of sideband acoustic response before and after MRCFM optimization: (<b>a</b>) Fixed carrier frequency modulation; (<b>b</b>) Markov chain random carrier frequency modulation.</p>
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<p>Comparison of simulated and measured peak sideband acoustic response for different modulation strategies.</p>
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22 pages, 5984 KiB  
Article
Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering
by Wenjiang Shao and Xiaowei Zhang
Appl. Sci. 2024, 14(11), 4617; https://doi.org/10.3390/app14114617 - 27 May 2024
Viewed by 757
Abstract
Subspace clustering algorithms have demonstrated remarkable success across diverse fields, including object segmentation, gene clustering, and recommendation systems. However, they often face challenges, such as omitting cluster information and the neglect of higher-order neighbor relationships within the data. To address these issues, a [...] Read more.
Subspace clustering algorithms have demonstrated remarkable success across diverse fields, including object segmentation, gene clustering, and recommendation systems. However, they often face challenges, such as omitting cluster information and the neglect of higher-order neighbor relationships within the data. To address these issues, a novel subspace clustering method named Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering is proposed. This method seamlessly embeds Markov transition probability information into the self-expression, leveraging a fine-grained neighbor matrix to uncover latent data structures. This matrix preserves crucial high-order local information and complementary details, ensuring a comprehensive understanding of the data. To effectively handle complex nonlinear relationships, the method learns the underlying manifold structure from a cross-order local neighbor graph. Additionally, connectivity constraints are applied to the affinity matrix, enhancing the group structure and further improving the clustering performance. Extensive experiments demonstrate the superiority of this novel method over baseline approaches, validating its effectiveness and practical utility. Full article
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<p>Visual illustration of neighbor relationships of different orders.</p>
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<p>The flowchart of Markov-Embedded Affinity Learning with Connectivity Constraints for Subspace Clustering (MKSC).</p>
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<p>Examples of images selected from three different real application data sets.</p>
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<p>Examples of moon data set.</p>
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<p>Time costs of different methods on various data sets.</p>
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<p>Examples of the learned representation matrix <span class="html-italic">Z</span>.</p>
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<p>The t-SNE visualization of the Jaffe and PIX data sets, respectively. The first and second rows correspond to the t-SNE visualization of the original data and the reconstructed representation on Jaffe and PIX, respectively.</p>
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<p>Examples to show the convergence of <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>Z</mi> <mi>t</mi> </msub> <mo>}</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi>B</mi> <mi>t</mi> </msub> <mo>}</mo> </mrow> </semantics></math> on different data sets.</p>
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<p>Results of comparison between MKSC and comparison method on MNIST and Semeion.</p>
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<p>Results of comparison between MKSC and comparison method on ORL and Alphadigit.</p>
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<p>Results of comparison between MKSC and comparison method on ORL, MNIST, and StillDB.</p>
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<p>Clustering performance of MKSC with combination of <math display="inline"><semantics> <mrow> <mo>{</mo> <mi>α</mi> <mo>,</mo> <mi>ζ</mi> <mo>}</mo> </mrow> </semantics></math> on MNIST data set.</p>
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<p>Clustering performance of MKSC with combination of <math display="inline"><semantics> <mrow> <mo>{</mo> <mi>β</mi> <mo>,</mo> <mi>γ</mi> <mo>}</mo> </mrow> </semantics></math> on MNIST data set.</p>
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<p>Comparison of data reconstruction effects. The first and second rows correspond to the effects of the original and reconstructed data, respectively.</p>
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13 pages, 1279 KiB  
Article
Fault Distance Measurement in Distribution Networks Based on Markov Transition Field and Darknet-19
by Haozhi Wang, Wei Guo and Yuntao Shi
Mathematics 2024, 12(11), 1665; https://doi.org/10.3390/math12111665 - 27 May 2024
Cited by 2 | Viewed by 792
Abstract
The modern distribution network system is gradually becoming more complex and diverse, and traditional fault location methods have difficulty in quickly and accurately locating the fault location after a single-phase ground fault occurs. Therefore, this study proposes a new solution based on the [...] Read more.
The modern distribution network system is gradually becoming more complex and diverse, and traditional fault location methods have difficulty in quickly and accurately locating the fault location after a single-phase ground fault occurs. Therefore, this study proposes a new solution based on the Markov transfer field and deep learning to predict the fault location, which can accurately predict the location of a single-phase ground fault in the distribution network. First, a new phase-mode transformation matrix is used to take the fault current of the distribution network as the modulus 1 component, avoiding complex calculations in the complex field; then, the extracted modulus 1 component of the current is transformed into a Markov transfer field and converted into an image using pseudo-color coding, thereby fully exploiting the fault signal characteristics; finally, the Darknet-19 network is used to automatically extract fault features and predict the distance of the fault occurrence. Through simulations on existing models and training and testing with a large amount of data, the experimental results show that this method has good stability, high accuracy, and strong anti-interference ability. This solution can effectively predict the distance of ground faults in distribution networks. Full article
(This article belongs to the Special Issue Complex Process Modeling and Control Based on AI Technology)
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<p>The MTF transformation process.</p>
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<p>The Darknet-19 network model.</p>
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<p>The feature extraction process in Darknet-19.</p>
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<p>MTF images of distribution network ground faults at different distances.</p>
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<p>Fault distance measurement process.</p>
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<p>Training and validation loss function curves of the Darknet-19 model.</p>
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<p>Physical simulation of fault distance detection.</p>
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12 pages, 2036 KiB  
Article
A Lightweight Convolutional Neural Network Method for Two-Dimensional PhotoPlethysmoGraphy Signals
by Feng Zhao, Xudong Zhang and Zhenyu He
Appl. Sci. 2024, 14(10), 3963; https://doi.org/10.3390/app14103963 - 7 May 2024
Cited by 1 | Viewed by 1043
Abstract
Data information security on wearable devices has emerged as a significant concern among users, so it becomes urgent to explore authentication methods based on wearable devices. Using PhotoPlethysmoGraphy (PPG) signals for identity authentication has been proven effective in biometric authentication. This paper proposes [...] Read more.
Data information security on wearable devices has emerged as a significant concern among users, so it becomes urgent to explore authentication methods based on wearable devices. Using PhotoPlethysmoGraphy (PPG) signals for identity authentication has been proven effective in biometric authentication. This paper proposes a convolutional neural network authentication method based on 2D PPG signals applied to wearable devices. This method uses Markov Transition Field technology to convert one-dimensional PPG signal data into two-dimensional image data, which not only retains the characteristics of the signal but also enriches the spatial information. Afterward, considering that wearable devices usually have limited resources, a lightweight convolutional neural network model is also designed in this method, which reduces resource consumption and computational complexity while ensuring high performance. It is proved experimentally that this method achieves 98.62% and 96.17% accuracy on the training set and test set, respectively, an undeniable advantage compared to the traditional one-dimensional deep learning method and the classical two-dimensional deep learning method. Full article
(This article belongs to the Special Issue Machine Learning Based Biomedical Signal Processing)
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<p>Overall methodology flowchart for identity authentication using PPG signals.</p>
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<p>Conversion of one-dimensional data to two-dimensional.</p>
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<p>Illustration of Depthwise Separable Convolution.</p>
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<p>Schematic diagram of the residual structure.</p>
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<p>Illustration of the Lightweight Convolutional Neural Network (LW-CNN).</p>
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<p>LW-CNN Accuracy (<b>a</b>) and Loss (<b>b</b>) Curves.</p>
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<p>Confusion matrix of LW-CNN.</p>
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18 pages, 1921 KiB  
Article
Wide-TSNet: A Novel Hybrid Approach for Bitcoin Price Movement Classification
by Peter Tettey Yamak, Yujian Li, Ting Zhang and Pius K. Gadosey
Appl. Sci. 2024, 14(9), 3797; https://doi.org/10.3390/app14093797 - 29 Apr 2024
Viewed by 1424
Abstract
In this paper, we introduce Wide-TSNet, a novel hybrid approach for predicting Bitcoin prices using time-series data transformed into images. The method involves converting time-series data into Markov transition fields (MTFs), enhancing them using histogram equalization, and classifying them using Wide ResNets, a [...] Read more.
In this paper, we introduce Wide-TSNet, a novel hybrid approach for predicting Bitcoin prices using time-series data transformed into images. The method involves converting time-series data into Markov transition fields (MTFs), enhancing them using histogram equalization, and classifying them using Wide ResNets, a type of convolutional neural network (CNN). We propose a tripartite classification system to accurately represent Bitcoin price trends. In addition, we demonstrate the effectiveness of Wide-TSNet through various experiments, in which it achieves an Accuracy of approximately 94% and an F1 score of 90%. It is also shown that lightweight CNN models, such as SqueezeNet and EfficientNet, can be as effective as complex models under certain conditions. Furthermore, we investigate the efficacy of other image transformation methods, such as Gramian angular fields, in capturing the trends and volatility of Bitcoin prices and revealing patterns that are not visible in the raw data. Moreover, we assess the effect of image resolution on model performance, emphasizing the importance of this factor in image-based time-series classification. Our findings explore the intersection between finance, image processing, and deep learning, providing a robust methodology for financial time-series classification. Full article
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<p>Wide-TSNet framework diagram.</p>
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<p>Sample Markov transition fields of the Bitcoin time-series data in grayscale and RGB.</p>
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<p>Comparison of original and histogram equalized image.</p>
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<p>A simple convolutional neural network framework.</p>
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<p>Plot of the closing price from the Bitcoin data set.</p>
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<p>Effect of image size on the classification accuracy of the various classifiers, as compared to Wide-TSNet: (<b>a</b>) Wide ResNet; (<b>b</b>) EfficientNet; and (<b>c</b>) SqueezeNet.</p>
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16 pages, 4093 KiB  
Article
Sea-Surface Small Target Detection Based on Improved Markov Transition Fields
by Ru Ye, Hongyan Xing and Xing Zhou
J. Mar. Sci. Eng. 2024, 12(4), 582; https://doi.org/10.3390/jmse12040582 - 29 Mar 2024
Cited by 1 | Viewed by 1019
Abstract
Addressing the limitations of manually extracting features from small maritime target signals, this paper explores Markov transition fields and convolutional neural networks, proposing a detection method for small targets based on an improved Markov transition field. Initially, the raw data undergo a Fourier [...] Read more.
Addressing the limitations of manually extracting features from small maritime target signals, this paper explores Markov transition fields and convolutional neural networks, proposing a detection method for small targets based on an improved Markov transition field. Initially, the raw data undergo a Fourier transform, feature fusion is performed on the series, and a spectrogram is generated using Markov transition fields to extract radar data features from both the time domain and frequency domain, providing a more comprehensive data representation for the detector. Then, the InceptionResnetV2 network is employed as a classifier, setting decision thresholds based on the softmax layer’s output, thus achieving controllable false alarms in the detection of small maritime targets. Additionally, transfer learning is introduced to address the issue of sample imbalance. The IPIX dataset is used for experimental verification. The experimental results show that the proposed detection method can deeply mine the differences between targets and the maritime clutter background, demonstrating superior detection performance. When the observation time is set to 1.024 s, the IMIRV2 detector performs best. Cross-validation with different data preprocessing methods and classification models reveals a significant advantage in the performance of the IMIRV2 detector, especially at low signal-to-noise ratios. Finally, a comparison with the performance of existing detectors indicates that the proposed method offers certain improvements. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Data transformation based on improved MTF. (<b>a</b>) Transformation of the pure clutter; (<b>b</b>) Transformation of the pure clutter with target returns.</p>
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<p>Target Detection Model Diagram Based on Improved MTF-InceptionResNetV2.</p>
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<p>Data transformation based on MTF and improved MTF. (<b>a</b>) Transformation of the pure clutter; (<b>b</b>) Transformation of the pure clutter with target returns.</p>
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<p>InceptionResNetV2 Model Diagram.</p>
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<p>False Alarm Controllable Decision Area.</p>
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<p>ASCR under The Four Types of Polarization.</p>
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<p>Detection Probability under Different Data Dimensionalities.</p>
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<p>Improved RP: (<b>a</b>) Specific steps of the improved RP method, (<b>b</b>) Comparative images before and after the improvement of RP.</p>
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<p>Improved GAF: (<b>a</b>) Specific steps of the improved GAF method, (<b>b</b>) Comparative images before and after the improvement of GAF.</p>
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<p>Detector performance under different preprocessing methods.</p>
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<p>Comparison of detection performance of four types of detectors: (<b>a</b>) Detection performance under HH polarization condition, (<b>b</b>) Detection performance under HV polarization condition, (<b>c</b>) Detection performance under VH polarization condition, (<b>d</b>) Detection performance under VV polarization condition.</p>
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14 pages, 2649 KiB  
Article
Improved SE-ResNet Acoustic–Vibration Fusion for Rolling Bearing Composite Fault Diagnosis
by Xiaojiao Gu, Yang Tian, Chi Li, Yonghe Wei and Dashuai Li
Appl. Sci. 2024, 14(5), 2182; https://doi.org/10.3390/app14052182 - 5 Mar 2024
Cited by 5 | Viewed by 1449
Abstract
An enhanced fault diagnosis approach for rolling bearings with composite faults using an optimized Squeeze and Excitation ResNet (SE-ResNet) model is proposed. This method integrates grid search (GS), support vector regression (SVR), ensemble empirical mode decomposition (EEMD), and low-rank multimodal fusion (LMF) to [...] Read more.
An enhanced fault diagnosis approach for rolling bearings with composite faults using an optimized Squeeze and Excitation ResNet (SE-ResNet) model is proposed. This method integrates grid search (GS), support vector regression (SVR), ensemble empirical mode decomposition (EEMD), and low-rank multimodal fusion (LMF) to effectively handle the signals of acoustic–vibration fusion. By combining these techniques, the aim is to improve the accuracy and reliability of rolling bearing fault diagnosis. Firstly, improved EEMD combined with GS-SVR and a window function is used for rolling bearing vibration signal decomposition. Singular value methods are used to filter and reconstruct the results. Secondly, Markov transition fields (MTFs) are used to encode vibration signals into 2D images. LMF is used for the fusion of vibration and sound signals. An improved Squeeze and Excitation ResNet50 network is proposed for feature identification and classification of rolling bearing composite fault data. Finally, the method undergoes rigorous testing and evaluation using rolling bearing data. The experimental outcomes demonstrate that, in comparison to traditional neural networks, the enhanced SE-ResNet, integrated with GS-SVR-EEMD and LMF, attains superior diagnostic accuracy. Additionally, the proposed approach can be effectively utilized for diagnosing rolling bearing composite faults. Full article
(This article belongs to the Section Acoustics and Vibrations)
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<p>Low-rank multimodal fusion.</p>
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<p>Squeeze and Extraction Module.</p>
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<p>Excitation operation.</p>
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<p>Test rig.</p>
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<p>Sensor arrangement.</p>
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<p>Bearing fault conditions: (<b>a</b>) outer race fault and (<b>b</b>) inner race fault.</p>
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<p>Diagnosis flowchart.</p>
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<p>Diagram of acoustic–vibration fusion: (<b>a</b>) composite fault; (<b>b</b>) inner ring fault; (<b>c</b>) outer ring fault; and (<b>d</b>) normal state.</p>
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<p>Training accuracy.</p>
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<p>Loss comparison.</p>
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22 pages, 23017 KiB  
Article
Dynamical Analysis of an Improved Bidirectional Immunization SIR Model in Complex Network
by Shixiang Han, Guanghui Yan, Huayan Pei and Wenwen Chang
Entropy 2024, 26(3), 227; https://doi.org/10.3390/e26030227 - 2 Mar 2024
Cited by 1 | Viewed by 1635
Abstract
In order to investigate the impact of two immunization strategies—vaccination targeting susceptible individuals to reduce their infection rate and clinical medical interventions targeting infected individuals to enhance their recovery rate—on the spread of infectious diseases in complex networks, this study proposes a bilinear [...] Read more.
In order to investigate the impact of two immunization strategies—vaccination targeting susceptible individuals to reduce their infection rate and clinical medical interventions targeting infected individuals to enhance their recovery rate—on the spread of infectious diseases in complex networks, this study proposes a bilinear SIR infectious disease model that considers bidirectional immunization. By analyzing the conditions for the existence of endemic equilibrium points, we derive the basic reproduction numbers and outbreak thresholds for both homogeneous and heterogeneous networks. The epidemic model is then reconstructed and extensively analyzed using continuous-time Markov chain (CTMC) methods. This analysis includes the investigation of transition probabilities, transition rate matrices, steady-state distributions, and the transition probability matrix based on the embedded chain. In numerical simulations, a notable concordance exists between the outcomes of CTMC and mean-field (MF) simulations, thereby substantiating the efficacy of the CTMC model. Moreover, the CTMC-based model adeptly captures the inherent stochastic fluctuation in the disease transmission, which is consistent with the mathematical properties of Markov chains. We further analyze the relationship between the system’s steady-state infection density and the immunization rate through MCS. The results suggest that the infection density decreases with an increase in the immunization rate among susceptible individuals. The current research results will enhance our understanding of infectious disease transmission patterns in real-world scenarios, providing valuable theoretical insights for the development of epidemic prevention and control strategies. Full article
(This article belongs to the Section Complexity)
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<p>Comparison of the <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> proportions through mean-field (MF) simulation method with and without the involvement of newly susceptible individuals in the epidemics spreading at each time step <span class="html-italic">t</span>. (<b>a</b>) Homogeneous networks, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>b</b>) heterogeneous networks, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. Setup of other parameters is <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>=</mo> <mn>0.08</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.175</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>. The number of infected and recovered individuals at initial time step is <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
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<p>Comparison of the evolution curves of the proportions of <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> based on MCS and CTMC methods at each time step on homogeneous networks with average degree <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. (<b>a</b>) Local amplification of Infected-MCS; (<b>b</b>) local amplification of Infected-CTMC; (<b>c</b>) local amplification of Recovered-MCS; (<b>d</b>) local amplification of Recovered-CTMC. Setup of other parameters is same as <a href="#entropy-26-00227-f001" class="html-fig">Figure 1</a>.</p>
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<p>Comparison of the evolution curves for the proportions of <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> through MCS and CTMC methods at each time step on heterogeneous networks with average degree <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. (<b>a</b>) Local amplification of Infected-MCS; (<b>b</b>) local amplification of Infected-CTMC; (<b>c</b>) local amplification of Recovered-MCS; (<b>d</b>) local amplification of Recovered-CTMC. Setup of other parameters is same as <a href="#entropy-26-00227-f001" class="html-fig">Figure 1</a>.</p>
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<p>Comparison of the evolution curves for the proportions of <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> through MF and CTMC methods at each time step on homogeneous and heterogeneous networks with average degree <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. (<b>a</b>) Homogeneous networks, local amplification of <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>; (<b>b</b>) homogeneous networks, local amplification of <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>; (<b>c</b>) heterogeneous networks, local amplification of <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>; (<b>d</b>) heterogeneous networks, local amplification of <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>. Setup of other parameters is same as <a href="#entropy-26-00227-f001" class="html-fig">Figure 1</a>.</p>
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<p>Comparison of the fraction of <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> with and without immunization measures over time, in BA networks with varying average degree <math display="inline"><semantics> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>. Setup of other parameters is same as <a href="#entropy-26-00227-f001" class="html-fig">Figure 1</a>. As average degree <math display="inline"><semantics> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> </semantics></math> increases, the impact of bidirectional immunization measures on epidemic spreading gradually diminishes.</p>
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<p>Fraction of <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> at steady state on ER and BA networks as a function of <math display="inline"><semantics> <mi>δ</mi> </semantics></math> for distinct values of <math display="inline"><semantics> <mi>β</mi> </semantics></math>. (<b>a</b>) ER network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>b</b>) ER network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>; (<b>c</b>) BA network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>d</b>) BA network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>. Setup of other parameters is same as <a href="#entropy-26-00227-f001" class="html-fig">Figure 1</a>. An augmentation in the parameter <math display="inline"><semantics> <mi>δ</mi> </semantics></math> leads to a discernible decrease in the magnitude of epidemic propagation in both ER and BA networks.</p>
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<p>Fraction of <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> at steady state on ER and BA networks as a function of <math display="inline"><semantics> <mi>δ</mi> </semantics></math> for distinct values of <math display="inline"><semantics> <mi>β</mi> </semantics></math>. (<b>a</b>) ER network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>b</b>) ER network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>; (<b>c</b>) BA network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>d</b>) BA network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>8</mn> </mrow> </semantics></math>. Setup of other parameters is same as <a href="#entropy-26-00227-f001" class="html-fig">Figure 1</a>. With the incremental rise in <math display="inline"><semantics> <mi>δ</mi> </semantics></math>, there is a notable augmentation in the magnitude of <math display="inline"><semantics> <mrow> <mi>S</mi> <mo>(</mo> <mo>∞</mo> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Fraction of <math display="inline"><semantics> <mrow> <mi>I</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> at each time step on different types of network datasets under various propagation models. (<b>a</b>) ER network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>b</b>) BA network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>c</b>) Facebook social network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>43.69</mn> </mrow> </semantics></math>; (<b>d</b>) Eneon mail communication network, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>10.02</mn> </mrow> </semantics></math>. Setup of other parameters is same as <a href="#entropy-26-00227-f001" class="html-fig">Figure 1</a>. In various datasets, bidirectional immunization measures can effectively reduce the infection peaks and steady-state infection density of epidemics.</p>
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<p>Comparison of the basic reproduction number <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math> in homogeneous and heterogeneous networks: impact of epidemic spreading parameters, bidirectional immunization rates and the rates of birth and death. (<b>a</b>) Variations in <math display="inline"><semantics> <mi>β</mi> </semantics></math> and <math display="inline"><semantics> <mi>γ</mi> </semantics></math>, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>b</b>) variations in <math display="inline"><semantics> <mi>δ</mi> </semantics></math> and <math display="inline"><semantics> <mi>λ</mi> </semantics></math>, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>; (<b>c</b>) variations in <span class="html-italic">b</span> and <span class="html-italic">d</span>, <math display="inline"><semantics> <mrow> <mfenced open="&#x2329;" close="&#x232A;"> <mi>k</mi> </mfenced> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. Setup of other parameters is same as <a href="#entropy-26-00227-f001" class="html-fig">Figure 1</a>.</p>
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18 pages, 2272 KiB  
Review
Application of Mass Service Theory to Economic Systems Optimization Problems—A Review
by Farida F. Galimulina and Naira V. Barsegyan
Mathematics 2024, 12(3), 403; https://doi.org/10.3390/math12030403 - 26 Jan 2024
Cited by 1 | Viewed by 1382
Abstract
An interdisciplinary approach to management allows for the integration of knowledge and tools of different fields of science into a unified methodology in order to improve the efficiency of resource management of different kinds of systems. In the conditions of global transformations, it [...] Read more.
An interdisciplinary approach to management allows for the integration of knowledge and tools of different fields of science into a unified methodology in order to improve the efficiency of resource management of different kinds of systems. In the conditions of global transformations, it is economic systems that have been significantly affected by external destabilizing factors. This determines the focus of attention on the need to develop tools for the modeling and optimization of economic systems, both in terms of organizational structure and in the context of resource management. The purpose of this review study is to identify the current gaps (shortcomings) in the scientific literature devoted to the issues of the modeling and optimization of economic systems using the tools of mass service theory. This article presents a critical analysis of approaches for the formulation of provisions on mass service systems in the context of resource management. On the one hand, modern works are characterized by the inclusion of an extensive number of random factors that determine the performance and efficiency of economic systems: the probability of delays and interruptions in mobile networks; the integration of order, inventory, and production management processes; the cost estimation of multi-server system operation; and randomness factors, customer activity, and resource constraints, among others. On the other hand, controversial points are identified. The analytical study carried out allows us to state that the prevailing majority of mass service models applied in relation to economic systems and resource supply optimization are devoted to Markov chain modeling. In terms of the chronology of the problems studied, there is a marked transition from modeling simple systems to complex mass service networks. In addition, we conclude that the complex architecture of modern economic systems opens up a wide research field for finding a methodology for assessing the dependence of the enterprise performance on the effect of optimization provided by using the provisions of mass service theory. This statement can be the basis for future research. Full article
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Figure 1

Figure 1
<p>The flowchart of the survey study.</p>
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<p>Advantages and disadvantages of methods of designing organizational management structures (summarized by the authors).</p>
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<p>Outlying parameters and performance indicators of methods for assessing organizational management structures (summarized by the authors).</p>
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<p>Organizational structure model in the form of a mass service system [<a href="#B50-mathematics-12-00403" class="html-bibr">50</a>].</p>
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<p>Modeling of the organizational structure of management in the form of a mass service network: (<b>a</b>) mass service network of the divisional organizational structure of management of a petrochemical enterprise; (<b>b</b>) mass service network of the project organizational structure of management of a petrochemical enterprise (proposed by the authors).</p>
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