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Search Results (3,513)

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Keywords = multi-order systems

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15 pages, 479 KiB  
Article
A Class of Distributed Online Aggregative Optimization in Unknown Dynamic Environment
by Chengqian Yang, Shuang Wang, Shuang Zhang, Shiwei Lin and Bomin Huang
Mathematics 2024, 12(16), 2460; https://doi.org/10.3390/math12162460 - 8 Aug 2024
Viewed by 281
Abstract
This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative [...] Read more.
This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative optimization problem more challenging. A distributed online optimization algorithm is designed for the considered problem via the mirror descent algorithm and the distributed average tracking method. In particular, the dynamic environment and the gradient are estimated by the averaged tracking methods, and then an online optimization algorithm is designed via a dynamic mirror descent method. It is shown that the dynamic regret is bounded in the order of O(T). Finally, the effectiveness of the designed algorithm is verified by some simulations of cooperative control of a multi-robot system. Full article
(This article belongs to the Topic Distributed Optimization for Control)
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<p>The concept of the cooperative control problem for a multi-robot system.</p>
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<p>Trajectories of <math display="inline"><semantics> <msubsup> <mi>x</mi> <mi>t</mi> <mo>∗</mo> </msubsup> </semantics></math> and <math display="inline"><semantics> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>t</mi> </mrow> </msub> </semantics></math> over <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math>.</p>
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<p>The dynamic regret of Algorithm 1 for problem (14) with constraint (15).</p>
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16 pages, 4331 KiB  
Article
MSD: Multi-Order Semantic Denoising Model for Session-Based Recommendations
by Shulin Cheng, Wentao Huang, Zhenqiang Yu and Jianxing Zheng
Electronics 2024, 13(16), 3118; https://doi.org/10.3390/electronics13163118 - 7 Aug 2024
Viewed by 319
Abstract
Session-based recommendations which aim to predict subsequent user–item interactions based on historical user behaviour during anonymous sessions can be challenging to carry out. Two main challenges need to be addressed and improved: (1) how does one analyze these sessions to accurately and completely [...] Read more.
Session-based recommendations which aim to predict subsequent user–item interactions based on historical user behaviour during anonymous sessions can be challenging to carry out. Two main challenges need to be addressed and improved: (1) how does one analyze these sessions to accurately and completely capture users’ preferences, and (2) how does one identify and eliminate any interference caused by noisy behavior? Existing methods have not adequately addressed these issues since they either neglect the valuable insights that can be gained from analyzing consecutive groups of items or fail to take these noisy data in sessions seriously and handle them properly, which can jointly impede recommendation systems from capturing users’ real intentions. To address these two problems, we designed a multi-order semantic denoising (MSD) model for session-based recommendations. Specifically, we grouped items of different lengths into varying multi-order semantic units to mine the user’s primary intentions from multiple dimensions. Meanwhile, a novel denoising network was designed to alleviate the interference of noisy behavior and provide a more precise session representation. The results of extensive experiments on three real-world datasets demonstrated that the proposed MSD model exhibited improved performance compared with existing state-of-the-art methods in session-based recommendations. Full article
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<p>Instances of items clicked by mistake or out of curiosity, which negatively impact the generation of reliable recommendations.</p>
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<p>The framework of the proposed MSD model.</p>
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<p>The performance of different orders.</p>
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<p>The performance of denoising depths.</p>
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29 pages, 8853 KiB  
Article
A Systems Biology Analysis of Chronic Lymphocytic Leukemia
by Giulia Pozzati, Jinrui Zhou, Hananel Hazan, Giannoula Lakka Klement, Hava T. Siegelmann, Jack A. Tuszynski and Edward A. Rietman
Onco 2024, 4(3), 163-191; https://doi.org/10.3390/onco4030013 - 6 Aug 2024
Viewed by 301
Abstract
Whole-genome sequencing has revealed that TP53, NOTCH1, ATM, SF3B1, BIRC3, ABL, NXF1, BCR, and ZAP70 are often mutated in CLL, but not consistently across all CLL patients. This paper employs a statistical thermodynamics approach in combination with the systems biology of the CLL [...] Read more.
Whole-genome sequencing has revealed that TP53, NOTCH1, ATM, SF3B1, BIRC3, ABL, NXF1, BCR, and ZAP70 are often mutated in CLL, but not consistently across all CLL patients. This paper employs a statistical thermodynamics approach in combination with the systems biology of the CLL protein–protein interaction networks to identify the most significant participant proteins in the cancerous transformation. Betti number (a topology of complexity) estimates highlight a protein hierarchy, primarily in the Wnt pathway known for aberrant CLL activation. These individually identified proteins suggest a network-targeted strategy over single-target drug development. The findings advocate for a multi-target inhibition approach, limited to several key proteins to minimize side effects, thereby providing a foundation for designing therapies. This study emphasizes a shift towards a comprehensive, multi-scale analysis to enhance personalized treatment strategies for CLL, which could be experimentally validated using siRNA or small-molecule inhibitors. The result is not just the identification of these proteins but their rank-order, offering a potent signal amplification in the context of the 20,000 proteins produced by the human body, thus providing a strategic basis for therapeutic intervention in CLL, underscoring the necessity for a more holistic, cellular, chromosomal, and genome-wide study to develop tailored treatments for CLL patients. Full article
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<p>As the “filtration plane” moves up from the bottom, more-and-more nodes are captured in larger-and-larger energetic subnetworks for protein–protein interaction set.</p>
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<p>Wnt signaling pathway from KEGG, <a href="https://www.genome.jp/pathway/hsa04310" target="_blank">https://www.genome.jp/pathway/hsa04310</a> accessed on 30 July 2024 [<a href="#B46-onco-04-00013" class="html-bibr">46</a>].</p>
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<p>The PPI of Wnt pathway.</p>
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<p>Pareto chart for Betti centrality at Gibbs-homology threshold-48, showing only those with nine or more occurrences.</p>
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<p>The Gibbs homology network for a patient in which RPS15 has the highest Betti centrality. RPS15 and MYC are pulled out for easy location. MYC and all of its first neighbors are highlighted in yellow.</p>
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<p>t-Distributed Stochastic Neighbor Embedding (t-SNE) analysis of CLL samples and subgroups. The visualization displays a non-linear dimensionality reduction of the complex gene expression data, with each point representing individual samples. The layout highlights the nuanced relationships and 10 clusters labeled from A to J within the CLL dataset, consisting of the 1001 patients, uncovering uncaptured subtleties through the network analysis. Samples included in the dataset are either diagnosed CLL patients (sick) or wild-type patients (normal) without CLL.</p>
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13 pages, 2893 KiB  
Review
Scanning Near-Field Optical Microscopy: Recent Advances in Disordered and Correlated Disordered Photonics
by Nicoletta Granchi
Photonics 2024, 11(8), 734; https://doi.org/10.3390/photonics11080734 - 6 Aug 2024
Viewed by 331
Abstract
Disordered and correlated disordered photonic materials have emerged in the past few decades and have been rapidly proposed as a complementary alternative to ordered photonics. These materials have thrived in the field of photonics, revealing the considerable impact of disorder with and without [...] Read more.
Disordered and correlated disordered photonic materials have emerged in the past few decades and have been rapidly proposed as a complementary alternative to ordered photonics. These materials have thrived in the field of photonics, revealing the considerable impact of disorder with and without structural correlations on the scattering, transport, and localization of light in matter. Scanning near-field optical microscopy (SNOM) has proven to be a fundamental tool for the study of the interaction between light and matter at the nanoscale in such systems, allowing for the investigation of optical properties and local electromagnetic fields with extremely high spatial resolution, surpassing the diffraction limit of conventional optical microscopy. In this review, the most important and recent advances obtained for disordered and correlated disordered luminescent structures by means of the aperture SNOM technique are addressed, showing how it allows the tailoring of local density of states (LDOS), as well as providing access to statistical analysis for multi-resonance disordered and hyperuniform disordered structures at telecom wavelengths. Full article
(This article belongs to the Special Issue Advances in Near-Field Optics: Fundamentals and Applications)
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<p>(<b>a</b>) SEM view of the sample. Inset: cross-section of the slab. A SNOM PL map evaluated at 1293 nm is overlapped with the SEM image. Different colors are used to highlight different photonic modes. (<b>b</b>) SNOM PL spectra normalized to the average PL of the entire map, acquired in correspondence with the four modes highlighted with different colors in (<b>a</b>). (<b>c</b>) Sketch of the nano-oxidation with SNOM probe. (<b>d</b>) SNOM PL spectra of the red and green modes previous and subsequent to oxidation. (<b>e</b>) Upper row: SNOM maps filtered at wavelength of the tuned mode before and after the oxidation process. Lower row: maps obtained through the Lorentzian fit of the PL red peak. The scale bars correspond to 1 µm. Reprinted with permission from [<a href="#B10-photonics-11-00734" class="html-bibr">10</a>].</p>
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<p>(<b>a</b>) Sketch of the double membrane photonic crystal cavity system and of the coupling principle leading to the formation of S and AS modes. (<b>b</b>) Linear relationship between the greatest displacement and the applied force calculated through the use of FEM simulation to study the deformation of the bridge induced by a localized force applied at its center. Reprinted with permission from [<a href="#B26-photonics-11-00734" class="html-bibr">26</a>]. Copyright by American Physical Society. (<b>c</b>) The photonic crystal molecule is experimentally actuated by the mechanical contact force generated by the tip, resulting in a decrease or increase in wavelength for the symmetric (antisymmetric) fundamental mode when the tip is moved higher. Reprinted with permission from [<a href="#B26-photonics-11-00734" class="html-bibr">26</a>]. Copyright by American Physical Society. (<b>d</b>) Sketch of the SNOM tuning of double membrane photonic system patterned with the random design. (<b>e</b>) Map (in color scale relative to the PL intensity) of typical spectra obtained for various upper membrane deformations and wavelengths at a particular spatial point on the membrane.</p>
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<p>(<b>a</b>) SEM image of the HuD network sample; the inset reports the PL emission spectrum from the QDs embedded in the membrane. (<b>b</b>) Typical PL enhancement spectrum at a specific tip position. The PBG spectral region and the spectral intervals where localized (2) and de-localized (3) modes are observed are denoted by labels 1, 2, and 3, respectively. (<b>c</b>) Map of the highest PL enhancement in the spectral range [1165–1265] nm, taken from an 8 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> </mrow> </semantics></math>m × 8 <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">μ</mi> </mrow> </semantics></math>m SNOM PL map, scanned at a 100 nm/px resolution. The positions of the spectra described in (<b>d</b>) are indicated by 1, 2, and 3. (<b>e</b>) PL enhancement maps at the resonances of peaks 1, 2, and 3, where λ = 1172 nm, λ = 1184 nm, and λ = 1191 nm. (<b>f</b>) Number of modes derived from SNOM (red diamonds) and computed using FEM simulations (purple diamonds) for various spectral ranges. (<b>g</b>) IPR with respect to wavelength for experimental values (shown by red dots) and eigenstates of the SEM design structure (represented by blue dots) derived by FEM simulations. (<b>h</b>) Calculated (green dots) and experimental Qs (red dots) obtained from wavelength-dependent fits. All figures reprinted with permission from [<a href="#B41-photonics-11-00734" class="html-bibr">41</a>]. Copyright by Wiley and Son.</p>
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<p>(<b>a</b>) PL spectra of four different modes collected in correspondence of the maximum intensity of each. Green color reports the spectra of the structure and purple reports the replica. (<b>b</b>,<b>c</b>) SNOM PL maps filtered around the central wavelengths of the green (purple) peaks for the structure (replica), specifically <math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> = 1203.3 nm (<math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> = 1204.6 nm), <math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> = 1209.0 nm <math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> = 1207.0 nm), and <math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> = 1258.0 nm (<math display="inline"><semantics> <mrow> <mi>λ</mi> </mrow> </semantics></math> = 1259.0 nm). All figures reprinted with permission from [<a href="#B41-photonics-11-00734" class="html-bibr">41</a>]. Copyright by Wiley and Son.</p>
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<p>(<b>a</b>) SEM top view image of the engineered cavity embedded in HuD environment. (<b>b</b>) SNOM topography of the sample. (<b>c</b>) Typical SNOM PL spectrum with the first four resonances visible, obtained on top of the cavity. (<b>d</b>) Electric field intensity distribution maps for the four resonances, simulated in 3D with FEM. (<b>e</b>) SNOM spectral shift maps displaying the LDOS of the four resonances. All scale bars correspond to 1 μm. Reprinted with permission from [<a href="#B42-photonics-11-00734" class="html-bibr">42</a>]. Copyright by American Physical Society.</p>
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11 pages, 245 KiB  
Review
Gastrointestinal and Hepatobiliary Manifestations Associated with Untreated Celiac Disease in Adults and Children: A Narrative Overview
by Herbert Wieser, Carolina Ciacci, Carlo Soldaini, Carolina Gizzi and Antonella Santonicola
J. Clin. Med. 2024, 13(15), 4579; https://doi.org/10.3390/jcm13154579 - 5 Aug 2024
Viewed by 489
Abstract
Celiac disease (CeD) is a chronic inflammatory disease of the small intestine, produced by ingesting dietary gluten products in susceptible people. Gluten causes an impairment of the mucosal surface and, consequently, an abnormal absorption of nutrients. Although malabsorption of essential nutrients is a [...] Read more.
Celiac disease (CeD) is a chronic inflammatory disease of the small intestine, produced by ingesting dietary gluten products in susceptible people. Gluten causes an impairment of the mucosal surface and, consequently, an abnormal absorption of nutrients. Although malabsorption of essential nutrients is a major risk factor for various CeD-associated morbidities, genetic, immunological, and environmental factors also play an important role. The clinical presentation of CeD widely varies and can range from asymptomatic to full-blown symptoms due to the multi-system nature of CeD. The typical gastrointestinal (GI) manifestations of CeD include abdominal pain, diarrhea, bloating, and weight loss, but several hepatobiliary manifestations and a poor nutritional status have also been described. Currently, a gluten-free diet (GFD) is the only current evidence-based treatment that leads to the complete recovery of mucosal damage and the reversibility of its progression. Conversely, undiagnosed CeD might have severe consequences in children as well as in adult patients. This narrative overview aims to characterize the GI and hepatobiliary manifestations, nutritional deficiencies, and delayed pediatric development associated with unrecognized CeD in order to identify it promptly. Moreover, the role of GFD and how it could prevent long-term complications of CeD are described. Full article
(This article belongs to the Special Issue Future Trends in the Diagnosis and Management of Celiac Disease)
12 pages, 4364 KiB  
Article
Modeling Fluid Flow in Ship Systems for Controller Tuning Using an Artificial Neural Network
by Nur Assani, Petar Matić, Danko Kezić and Nikolina Pleić
J. Mar. Sci. Eng. 2024, 12(8), 1318; https://doi.org/10.3390/jmse12081318 - 4 Aug 2024
Viewed by 336
Abstract
Flow processes onboard ships are common in order to transport fluids like oil, gas, and water. These processes are controlled by PID controllers, acting on the regulation valves as actuators. In case of a malfunction or refitting, a PID controller needs to be [...] Read more.
Flow processes onboard ships are common in order to transport fluids like oil, gas, and water. These processes are controlled by PID controllers, acting on the regulation valves as actuators. In case of a malfunction or refitting, a PID controller needs to be re-adjusted for the optimal control of the process. To avoid experimenting on operational real systems, models are convenient alternatives. When real-time information is needed, digital twin (DT) concepts become highly valuable. The aim of this paper is to analyze and determine the optimal NARX model architecture in order to achieve a higher-accuracy model of a ship’s flow process. An artificial neural network (ANN) was used to model the process in MATLAB. The experiments were performed using a multi-start approach to prevent overtraining. To prove the thesis, statistical analysis of the experimental results was performed. Models were evaluated for generalization using mean squared error (MSE), best fit, and goodness of fit (GoF) measures on two independent datasets. The results indicate the correlation between the number of input delays and the performance of the model. A permuted k-fold cross-validation analysis was used to determine the optimal number of voltage and flow delays, thus defining the number of model inputs. Permutations of training, test, and validation datasets were applied to examine bias due to the data arrangement during training. Full article
(This article belongs to the Special Issue Data-Driven Methods for Marine Structures)
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<p>Flow control system.</p>
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<p>Flowchart of the data sampling.</p>
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<p>Flowchart of the proposed methodology for training the ANN NARX models.</p>
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<p>Flowchart of the data preparation methodology and training of the ANN NARX models.</p>
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<p>Flowchart of the ANN NARX models’ testingon two new time–series datasets.</p>
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<p>Convergence of the MSE during training: (<b>a</b>) using 1st permutation of data; (<b>b</b>) using 2nd permutation of data; (<b>c</b>) using 3rd permutation of data; (<b>d</b>) using 4th permutation of data; (<b>e</b>) using 5th permutation of data; and (<b>f</b>) using 6th permutation of data.</p>
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<p>Time-response of the best-performing ANN NARX model compared to the previously developed TF model using additional test dataset 1.</p>
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<p>Response time of the best-performing ANN NARX model compared to the previously developed TF model using additional test dataset 2.</p>
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<p>Error plot of the best-performing ANN NARX model compared to the target values from test dataset 2.</p>
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26 pages, 586 KiB  
Article
Hard Successive Interference Cancellation for M-QAM MIMO Links in the Presence of Rayleigh Deep-Fading
by Avner Elgam, Meir Klemfner, Shachar Silon, Yossi Peretz and Yosef Pinhasi
Sensors 2024, 24(15), 5038; https://doi.org/10.3390/s24155038 - 3 Aug 2024
Viewed by 599
Abstract
In our paper, we propose a generalized version of the Alternating Projections Digital Hard Successive Interference Cancellation (AP-HSIC) algorithm that is capable of decoding any order of constellation M in an M-Quadrature Amplitude Modulation (QAM) system. Our approach applies to Rayleigh deep-fading Multiple-Input [...] Read more.
In our paper, we propose a generalized version of the Alternating Projections Digital Hard Successive Interference Cancellation (AP-HSIC) algorithm that is capable of decoding any order of constellation M in an M-Quadrature Amplitude Modulation (QAM) system. Our approach applies to Rayleigh deep-fading Multiple-Input Multiple-Output (MIMO) channels with high-level Additive White Gaussian Noise (AWGN). It can handle various destructive phenomena without restricting the number of antenna arrays in the transmitter/receiver. Importantly, it does not rely on closed-loop MIMO feedback or the need for Channel-State Information Transmission (CSIT). We have demonstrated the effectiveness of our approach and provided a Bit Error Rate (BER) analysis for 16-, 32-, and 64-QAM modulation systems. Real-time simulations showcase the differences and advantages of our proposed algorithm compared to the Multi-Group Space-Time Coding (MGSTC) decoding algorithm and the Lagrange Multipliers Hard Successive Interference Cancellation (LM-HSIC) algorithm, which we have also developed here. Additionally, our paper includes a mathematical analysis of the LM-HSIC algorithm. The AP-HSIC algorithm is not only effective and fast in decoding, including interference cancellation computational feedback, but it can also be integrated with any Linear Processing Complex Orthogonal Design (LPCOD) technique, including Complex Orthogonal Design (COD) schemes such as high-order Orthogonal Space–Time Block Code (OSTBC) with high-order QAM symbols. Full article
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<p>AP-HSIC algorithm flowchart.</p>
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<p>LM-HSIC algorithm flowchart.</p>
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<p>Plot graphs of BER performance vs. the average SNR that compares three iterations of the MGSTC algorithm and systematic iteration of the AP-HSIC algorithm under 16-QAM modulation in the presence of Rayleigh deep-fading and high-level AWGN.</p>
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<p>BER performance vs. the average SNR of three iterations of the MGSTC algorithm and systematic iterations of the AP-HSIC algorithm. (<b>a</b>) Plot graphs of BER performance vs. the average SNR that compares three iterations of the MGSTC algorithm and systematic iterations of the AP-HSIC algorithm under 32-QAM modulation in the presence of Rayleigh deep-fading and high-level AWGN. (<b>b</b>) Plot graphs of BER performance vs. the average SNR that compares three iterations of the MGSTC algorithm and systematic iterations of the AP-HSIC algorithm under 64-QAM modulation in the presence of Rayleigh deep-fading and high-level AWGN.</p>
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<p>Plot graphs of BER performance vs. the average SNR for three systematic iterations using the MGSTC algorithm and AP-HSIC algorithm. Each iteration is represented by 16-QAM, 32-QAM, and 64-QAM modulations, respectively. The performance was compared under the presence of Rayleigh deep-fading and high-level AWGN.</p>
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<p>Average number of iterations for each average SNR value of AP-HSIC under 16-QAM modulation in the presence of Rayleigh deep-fading and high-level AWGN.</p>
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<p>Plot graphs of BER performance vs. the average SNR for three systematic iterations using the LM-HSIC algorithm and AP-HSIC algorithm. Each iteration is represented by 16-QAM, 32-QAM, and 64-QAM modulations, respectively. The performance was compared under the presence of Rayleigh deep-fading and high-level AWGN.</p>
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<p>Comparisons of an average number of iterations for each average SNR value between LM-HSIC and AP-HSIC under 16-QAM modulation in the presence of Rayleigh deep-fading.</p>
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<p>Comparisons between BER performances vs. the average SNR of AP-HSIC under the scenarios of Rayleigh fading–SISO with 16-, 32-, and 64-QAM and the theoretical 16-, 32-, and 64-QAM SISO AWGN only, and between the scenarios of Rayleigh fading SISO 16-, 32-, and 64-QAM without any correction algorithm.</p>
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26 pages, 5746 KiB  
Article
A Novel SAR Imaging Method for GEO Satellite–Ground Bistatic SAR System with Severe Azimuth Spectrum Aliasing and 2-D Spatial Variability
by Jingjing Ti, Zhiyong Suo, Yi Liang, Bingji Zhao and Jiabao Xi
Remote Sens. 2024, 16(15), 2853; https://doi.org/10.3390/rs16152853 - 3 Aug 2024
Viewed by 478
Abstract
The satellite–ground bistatic configuration, which uses geosynchronous synthetic aperture radar (GEO SAR) for illumination and ground equipment for reception, can achieve wide coverage, high revisit, and continuous illumination of interest areas. Based on the analysis of the signal characteristics of GEO satellite–ground bistatic [...] Read more.
The satellite–ground bistatic configuration, which uses geosynchronous synthetic aperture radar (GEO SAR) for illumination and ground equipment for reception, can achieve wide coverage, high revisit, and continuous illumination of interest areas. Based on the analysis of the signal characteristics of GEO satellite–ground bistatic SAR (GEO SG-BiSAR), it is found that the bistatic echo signal has problems of azimuth spectrum aliasing and 2-D spatial variability. Therefore, to overcome those problems, a novel SAR imaging method for a GEO SG-BiSAR system with severe azimuth spectrum aliasing and 2-D spatial variability is proposed. Firstly, based on the geometric configuration of the GEO SG-BiSAR system, the time-domain and frequency-domain expressions of the signal are derived in detail. Secondly, in order to avoid the increasing cost caused by traditional multi-channel reception technology and the processing burden caused by inter-channel errors, the azimuth deramping is executed to solve the azimuth spectrum aliasing of the signal under the special geometric structure of GEO SG-BiSAR. Thirdly, based on the investigation of azimuth and range spatial variability characteristics of GEO SG-BiSAR in the Range Doppler (RD) domain, the azimuth spatial variability correction strategy is proposed. The signal corrected by the correction strategy has the same migration characteristics as monostatic radar. Therefore, the traditional chirp scaling function (CSF) is also modified to solve the range spatial variability of the signal. Finally, the two-dimensional spectrum of GEO SG-BiSAR with modified chirp scaling processing is derived, followed by the SPECAN operation to obtain the focused SAR image. Furthermore, the completed flowchart is also given to display the main composed parts for GEO SG-BiSAR imaging. Both azimuth spectrum aliasing and 2-D spatial variability are taken into account in the imaging method. The simulated data and the real data obtained by the Beidou navigation satellite are used to verify the effectiveness of the proposed method. Full article
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<p>Spatial observation geometric model of the GEO SG-BiSAR system.</p>
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<p>RD position model of GEO SG-BiSAR system.</p>
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<p>Target position obtained from GEO SG-BiSAR RD positioning equations.</p>
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<p>Azimuth spatial variation correction process for GEO SG-BiSAR.</p>
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<p>Range spatial variation schematic diagram of GEO SG-BiSAR signal.</p>
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<p>Processing flowchart for GEO SG-BiSAR imaging.</p>
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<p>Signals before and after azimuth deramping preprocessing. (<b>a</b>) Raw echo data. (<b>b</b>) Echo signal in the RD domain. (<b>c</b>) Signal after range compression. (<b>d</b>) Azimuth deramping preprocessed signal in time domain. (<b>e</b>) Azimuth deramping preprocessed signal in RD domain. (<b>f</b>) The range compression result of the azimuth deramping preprocessed signal.</p>
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<p>The two-dimensional spatial correction results of the azimuth preprocessed signal. (<b>a</b>) The range compression result of the azimuth preprocessed signal. (<b>b</b>) Signal after azimuth spatial variation correction. (<b>c</b>) Signal after range spatial variation correction. (<b>d</b>) The enlarged result of the red, block diagram in (<b>a</b>). (<b>e</b>) The enlarged result of the red, block diagram in (<b>b</b>). (<b>f</b>) The enlarged result of the red, block diagram in (<b>c</b>).</p>
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<p>SAR imaging result of the GEO SG-BiSAR simulation data.</p>
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<p>Comparison of imaging results obtained by traditional NLCS, BP, and the proposed method. (<b>a</b>) Imaging result of NLCS method. (<b>b</b>) Imaging result of BP method. (<b>c</b>) Imaging result of our proposed method.</p>
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<p>GEO SG-BiSAR navigation satellite experiment. (<b>a</b>) Experimental geometry configuration. (<b>b</b>) Optical photos of roof experiment field.</p>
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<p>Preprocessing results of the GEO SG-BiSAR navigation satellite experiment. (<b>a</b>) Capture result of the GEO SG-BiSAR navigation satellite. (<b>b</b>) Sky plot of the GEO SG-BiSAR navigation satellite.</p>
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<p>Imaging results of the GEO SG-BiSAR navigation satellite experiment. (<b>a</b>) Two-dimensional time-domain SAR signal. (<b>b</b>) The focused image of the repeater signal. (<b>c</b>) Azimuth pulse response of strong scattering point in (<b>b</b>). (<b>d</b>) Range pulse response of strong scattering point in (<b>b</b>).</p>
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25 pages, 1991 KiB  
Article
Chebyshev Pseudospectral Method for Fractional Differential Equations in Non-Overlapping Partitioned Domains
by Shina Daniel Oloniiju, Nancy Mukwevho, Yusuf Olatunji Tijani and Olumuyiwa Otegbeye
AppliedMath 2024, 4(3), 950-974; https://doi.org/10.3390/appliedmath4030051 - 2 Aug 2024
Viewed by 455
Abstract
Fractional differential operators are inherently non-local, so global methods, such as spectral methods, are well suited for handling these non-local operators. Long-time integration of differential models such as chaotic dynamical systems poses specific challenges and considerations that make multi-domain numerical methods advantageous when [...] Read more.
Fractional differential operators are inherently non-local, so global methods, such as spectral methods, are well suited for handling these non-local operators. Long-time integration of differential models such as chaotic dynamical systems poses specific challenges and considerations that make multi-domain numerical methods advantageous when dealing with such problems. This study proposes a novel multi-domain pseudospectral method based on the first kind of Chebyshev polynomials and the Gauss–Lobatto quadrature for fractional initial value problems.The proposed technique involves partitioning the problem’s domain into non-overlapping sub-domains, calculating the fractional differential operator in each sub-domain as the sum of the ‘local’ and ‘memory’ parts and deriving the corresponding differentiation matrices to develop the numerical schemes. The linear stability analysis indicates that the numerical scheme is absolutely stable for certain values of arbitrary non-integer order and conditionally stable for others. Numerical examples, ranging from single linear equations to systems of non-linear equations, demonstrate that the multi-domain approach is more appropriate, efficient and accurate than the single-domain scheme, particularly for problems with long-term dynamics. Full article
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Figure 1

Figure 1
<p>The boundaries of the closed disks in <a href="#appliedmath-04-00051-t001" class="html-table">Table 1</a>. The stability region of the linear discretization with two sub-domains for the indicated values of arbitrary non-integer order, (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.01</mn> <mo>,</mo> <mn>0.10</mn> <mo>,</mo> <mn>0.21</mn> <mo>,</mo> <mn>0.32</mn> <mo>,</mo> <mn>0.43</mn> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.54</mn> <mo>,</mo> <mn>0.65</mn> <mo>,</mo> <mn>0.76</mn> <mo>,</mo> <mn>0.87</mn> <mo>,</mo> <mn>0.98</mn> </mrow> </semantics></math>, lies outside these circles.</p>
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<p>The stability regions of quadratic approximations with <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.21</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.54</mn> </mrow> </semantics></math> and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.98</mn> </mrow> </semantics></math>. The stability regions are the shaded areas located outside the elliptical disks.</p>
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<p>The dynamics of the Bagley–Torvik Equation (<a href="#FD34-appliedmath-04-00051" class="html-disp-formula">34</a>) for various values of <math display="inline"><semantics> <mi>γ</mi> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>70</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>400</mn> </mrow> </semantics></math>: (<b>a</b>) the phase portrait for the <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>−</mo> <msup> <mi>u</mi> <mo>′</mo> </msup> </mrow> </semantics></math> plane and (<b>b</b>) the <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> profile.</p>
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<p>The phase portraits of the chaotic systems (<a href="#FD36-appliedmath-04-00051" class="html-disp-formula">36</a>) for the (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics></math> plane, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> surface with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>0.99</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>250</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>N</mi> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>850</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 4 Cont.
<p>The phase portraits of the chaotic systems (<a href="#FD36-appliedmath-04-00051" class="html-disp-formula">36</a>) for the (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics></math> plane, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> surface with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>0.99</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>250</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>N</mi> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>850</mn> </mrow> </semantics></math>.</p>
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<p>The time evolution of <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> of the chaotic system (<a href="#FD37-appliedmath-04-00051" class="html-disp-formula">37</a>) with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>1.00</mn> <mo>,</mo> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <msub> <mo>Ω</mo> <mn>1</mn> </msub> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>100</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>N</mi> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math>.</p>
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<p>The phase portraits of the chaotic system (<a href="#FD37-appliedmath-04-00051" class="html-disp-formula">37</a>) for the (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics></math> plane, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> surface with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>1.00</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mo>Ω</mo> <mn>1</mn> </msub> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>T</mi> <mo>=</mo> <mn>100</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>N</mi> <mo>=</mo> <mn>13</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math>.</p>
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<p>The phase portraits of the chaotic systems (<a href="#FD38-appliedmath-04-00051" class="html-disp-formula">38</a>) for the (<b>a</b>) <math display="inline"><semantics> <msub> <mi>u</mi> <mn>1</mn> </msub> </semantics></math>-<math display="inline"><semantics> <msub> <mi>u</mi> <mn>2</mn> </msub> </semantics></math> plane, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> surface with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.90</mn> <mo>,</mo> <mspace width="3.33333pt"/> <msub> <mo>Ψ</mo> <mn>1</mn> </msub> <mo>=</mo> <mn>0.4</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>T</mi> <mo>=</mo> <mn>200</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>N</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>900</mn> </mrow> </semantics></math>.</p>
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<p>The phase portraits of the chaotic systems (<a href="#FD39-appliedmath-04-00051" class="html-disp-formula">39</a>) for the (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics></math> plane, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> surface with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.95</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>T</mi> <mo>=</mo> <mn>150</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>N</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>800</mn> </mrow> </semantics></math>.</p>
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<p>The phase portraits of the chaotic systems (<a href="#FD39-appliedmath-04-00051" class="html-disp-formula">39</a>) for the (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> </semantics></math> plane, (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane, (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane and (<b>d</b>) <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </semantics></math> surface with <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.90</mn> <mspace width="3.33333pt"/> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mspace width="3.33333pt"/> <mn>0.95</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>T</mi> <mo>=</mo> <mn>80</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>N</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>350</mn> </mrow> </semantics></math>.</p>
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<p>The maximum residual error in each domain for (<b>a</b>) Equation (36) (<b>b</b>) Equation (37) (<b>c</b>) Equation (38) and (<b>d</b>) Equation (39) using <math display="inline"><semantics> <mrow> <mi>γ</mi> <mo>=</mo> <mn>0.8</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>T</mi> <mo>=</mo> <mn>50</mn> <mo>,</mo> <mspace width="3.33333pt"/> <mi>N</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>q</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math>.</p>
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51 pages, 3714 KiB  
Review
Network Security Challenges and Countermeasures for Software-Defined Smart Grids: A Survey
by Dennis Agnew, Sharon Boamah, Arturo Bretas and Janise McNair
Smart Cities 2024, 7(4), 2131-2181; https://doi.org/10.3390/smartcities7040085 - 2 Aug 2024
Viewed by 543
Abstract
The rise of grid modernization has been prompted by the escalating demand for power, the deteriorating state of infrastructure, and the growing concern regarding the reliability of electric utilities. The smart grid encompasses recent advancements in electronics, technology, telecommunications, and computer capabilities. Smart [...] Read more.
The rise of grid modernization has been prompted by the escalating demand for power, the deteriorating state of infrastructure, and the growing concern regarding the reliability of electric utilities. The smart grid encompasses recent advancements in electronics, technology, telecommunications, and computer capabilities. Smart grid telecommunication frameworks provide bidirectional communication to facilitate grid operations. Software-defined networking (SDN) is a proposed approach for monitoring and regulating telecommunication networks, which allows for enhanced visibility, control, and security in smart grid systems. Nevertheless, the integration of telecommunications infrastructure exposes smart grid networks to potential cyberattacks. Unauthorized individuals may exploit unauthorized access to intercept communications, introduce fabricated data into system measurements, overwhelm communication channels with false data packets, or attack centralized controllers to disable network control. An ongoing, thorough examination of cyber attacks and protection strategies for smart grid networks is essential due to the ever-changing nature of these threats. Previous surveys on smart grid security lack modern methodologies and, to the best of our knowledge, most, if not all, focus on only one sort of attack or protection. This survey examines the most recent security techniques, simultaneous multi-pronged cyber attacks, and defense utilities in order to address the challenges of future SDN smart grid research. The objective is to identify future research requirements, describe the existing security challenges, and highlight emerging threats and their potential impact on the deployment of software-defined smart grid (SD-SG). Full article
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Figure 1

Figure 1
<p>A software-defined smart grid (SD-SG) architecture.</p>
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<p>Overall structure of this survey.</p>
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<p>General SDN architecture.</p>
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<p>Taxonomy of SD-SG network security: cyberattacks and defense techniques (Current focus of research literature: DDoS/DoS Attacks Defense Techniques [<a href="#B37-smartcities-07-00085" class="html-bibr">37</a>,<a href="#B38-smartcities-07-00085" class="html-bibr">38</a>,<a href="#B39-smartcities-07-00085" class="html-bibr">39</a>,<a href="#B40-smartcities-07-00085" class="html-bibr">40</a>,<a href="#B41-smartcities-07-00085" class="html-bibr">41</a>,<a href="#B42-smartcities-07-00085" class="html-bibr">42</a>,<a href="#B43-smartcities-07-00085" class="html-bibr">43</a>,<a href="#B44-smartcities-07-00085" class="html-bibr">44</a>,<a href="#B45-smartcities-07-00085" class="html-bibr">45</a>,<a href="#B46-smartcities-07-00085" class="html-bibr">46</a>,<a href="#B47-smartcities-07-00085" class="html-bibr">47</a>,<a href="#B48-smartcities-07-00085" class="html-bibr">48</a>,<a href="#B49-smartcities-07-00085" class="html-bibr">49</a>,<a href="#B50-smartcities-07-00085" class="html-bibr">50</a>]; SDN Controller Attacks Defense Techniques [<a href="#B51-smartcities-07-00085" class="html-bibr">51</a>,<a href="#B52-smartcities-07-00085" class="html-bibr">52</a>,<a href="#B53-smartcities-07-00085" class="html-bibr">53</a>,<a href="#B54-smartcities-07-00085" class="html-bibr">54</a>,<a href="#B55-smartcities-07-00085" class="html-bibr">55</a>]; Multi-Pronged Attack Defense Techniques [<a href="#B5-smartcities-07-00085" class="html-bibr">5</a>,<a href="#B17-smartcities-07-00085" class="html-bibr">17</a>,<a href="#B36-smartcities-07-00085" class="html-bibr">36</a>,<a href="#B56-smartcities-07-00085" class="html-bibr">56</a>,<a href="#B57-smartcities-07-00085" class="html-bibr">57</a>,<a href="#B58-smartcities-07-00085" class="html-bibr">58</a>,<a href="#B59-smartcities-07-00085" class="html-bibr">59</a>,<a href="#B60-smartcities-07-00085" class="html-bibr">60</a>]; Grid Balancing Attacks Defense Techniques [<a href="#B61-smartcities-07-00085" class="html-bibr">61</a>,<a href="#B62-smartcities-07-00085" class="html-bibr">62</a>,<a href="#B63-smartcities-07-00085" class="html-bibr">63</a>,<a href="#B64-smartcities-07-00085" class="html-bibr">64</a>,<a href="#B65-smartcities-07-00085" class="html-bibr">65</a>]).</p>
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<p>Proposed SDN-integrated IEEE-14 bus system [<a href="#B77-smartcities-07-00085" class="html-bibr">77</a>].</p>
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<p>ClusterBlock design presented in [<a href="#B37-smartcities-07-00085" class="html-bibr">37</a>].</p>
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<p>Moving target defense example architecture.</p>
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<p>Software-defined smart grid (SD-SG) moving target defense (MTD) game example.</p>
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<p>Strategic interaction scenarios between a hypervisor and an attacker [<a href="#B55-smartcities-07-00085" class="html-bibr">55</a>] (<b>a</b>)—(<math display="inline"><semantics> <msub> <mi mathvariant="normal">m</mi> <mi>i</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi mathvariant="normal">a</mi> <mi>j</mi> </msub> </semantics></math>): <span class="html-italic">H</span> monitors the controller <math display="inline"><semantics> <msub> <mi mathvariant="normal">k</mi> <mi>i</mi> </msub> </semantics></math> &amp; <span class="html-italic">D</span> attacks <math display="inline"><semantics> <msub> <mi mathvariant="normal">k</mi> <mi>i</mi> </msub> </semantics></math>, where <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>≠</mo> <mi>j</mi> </mrow> </semantics></math>; (<b>b</b>)—(<math display="inline"><semantics> <msub> <mi mathvariant="normal">m</mi> <mrow> <mi>i</mi> <mo>=</mo> <mi>j</mi> </mrow> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi mathvariant="normal">a</mi> <mi>j</mi> </msub> </semantics></math>): <span class="html-italic">H</span> monitors <math display="inline"><semantics> <msub> <mi mathvariant="normal">k</mi> <mi>i</mi> </msub> </semantics></math> &amp; detects an instruction by <span class="html-italic">D</span> which attacks the same controller; (<b>c</b>)—(<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">m</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi mathvariant="normal">a</mi> <mi>j</mi> </msub> </mrow> </semantics></math>): <span class="html-italic">H</span> does not monitor any controller and an intrusion occurs on a controller <math display="inline"><semantics> <msub> <mi mathvariant="normal">k</mi> <mi>i</mi> </msub> </semantics></math> by <span class="html-italic">D</span>; (<b>d</b>)—(<math display="inline"><semantics> <msub> <mi mathvariant="normal">m</mi> <mi>b</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi mathvariant="normal">a</mi> <mn>0</mn> </msub> </semantics></math>): <span class="html-italic">H</span> monitors a controller <math display="inline"><semantics> <msub> <mi mathvariant="normal">k</mi> <mi>i</mi> </msub> </semantics></math> and <span class="html-italic">D</span> takes the action non-attack.</p>
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<p>Cross-layer cyber–physical security architecture presented in [<a href="#B36-smartcities-07-00085" class="html-bibr">36</a>].</p>
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<p>Flatly distributed SDN controller architecture.</p>
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<p>Botnet life cycle presented in [<a href="#B173-smartcities-07-00085" class="html-bibr">173</a>].</p>
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32 pages, 13228 KiB  
Article
Multi-Scale Higher-Order Dependencies (MSHOD): Higher-Order Interactions Mining and Key Nodes Identification for Global Liner Shipping Network
by Yude Fu, Xiang Li, Jichao Li, Mengjun Yu, Xiongyi Lu, Qizi Huangpeng and Xiaojun Duan
J. Mar. Sci. Eng. 2024, 12(8), 1305; https://doi.org/10.3390/jmse12081305 - 1 Aug 2024
Viewed by 325
Abstract
Liner shipping accounts for over 80% of the global transportation volume, making substantial contributions to world trade and economic development. To advance global economic integration further, it is essential to link the flows of global liner shipping routes with the complex system [...] Read more.
Liner shipping accounts for over 80% of the global transportation volume, making substantial contributions to world trade and economic development. To advance global economic integration further, it is essential to link the flows of global liner shipping routes with the complex system of international trade, thereby supporting liner shipping as an effective framework for analyzing international trade and geopolitical trends. Traditional methods based on first-order global liner shipping networks, operating at a single scale, lack sufficient descriptive power for multi-variable sequential interactions and data representation accuracy among nodes. This paper proposes an effective methodology termed “Multi-Scale Higher-Order Dependencies (MSHOD)” that adeptly reveals the complexity of higher-order interactions among multi-scale nodes within the global liner shipping network. The key step of this method is to construct high-order dependency networks through multi-scale attributes. Based on the critical role of high-order interactions, a method for key node identification has been proposed. Experiments demonstrate that, compared to other methods, MSHOD can more effectively identify multi-scale nodes with regional dependencies. These nodes and their generated higher-order interactions could have transformative impacts on the network’s flow and stability. Therefore, by integrating multi-scale analysis methods to mine high-order interactions and identify key nodes with regional dependencies, this approach provides robust insights for assessing policy implementation effects, preventing unforeseen incidents, and revealing regional dual-circulation economic models, thereby contributing to strategies for global, stable development. Full article
(This article belongs to the Topic Global Maritime Logistics in the Era of Industry 4.0)
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Figure 1
<p>Schematic of higher-order Markov properties in GLSRFs.</p>
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<p>BuildMSHODN algorithm. There are three steps in the algorithm: the extraction of higher-order dependency rules, edge reconfiguration, and the construction of higher-order dependency networks with multi-scale attributes.</p>
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<p>Correspondence between higher-order nodes and physical nodes.</p>
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<p>(<b>a</b>) SSFODN and (<b>b</b>) SSHODN (using part of Singapore’s connectivity as an example).</p>
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<p>Example of second-order dependency relationships in the SSHODN. (<b>a</b>–<b>d</b>) Nodes on either side representing paths with dependency relationships using Singapore (port) as the hub node (<math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mo>−</mo> <mi>S</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> <mi>a</mi> <mi>p</mi> <mi>o</mi> <mi>r</mi> <mi>e</mi> </mrow> </semantics></math>). The percentage on the left node indicates the proportion of <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math>. The percentage on the right node indicates the proportion of <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mi>r</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mi>z</mi> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math>.</p>
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<p>Example illustrating the importance of higher-order interactions in problem analysis.</p>
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<p>Third-order dependency relationships in SSHODN (using Shanghai as an example). (<b>a</b>–<b>d</b>) represent the nodes corresponding to the respective container ports.</p>
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<p><math display="inline"><semantics> <mo>Θ</mo> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mo>Θ</mo> <mo>˜</mo> </mover> </semantics></math> results for the top 20 container ports by global average annual throughput. (<b>a</b>,<b>b</b>) The results of analyzing different ports using <math display="inline"><semantics> <mo>Θ</mo> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mo>Θ</mo> <mo>˜</mo> </mover> </semantics></math>, respectively, where gray bars represent <math display="inline"><semantics> <mrow> <mi>B</mi> <mi>T</mi> <mi>P</mi> </mrow> </semantics></math>, green bars represent <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>n</mi> <mi>o</mi> <mi>t</mi> <mi>T</mi> </mrow> </semantics></math>, and pink lines indicate whether <math display="inline"><semantics> <mo>Θ</mo> </semantics></math> (<math display="inline"><semantics> <mover accent="true"> <mo>Θ</mo> <mo>˜</mo> </mover> </semantics></math>) is among the top 20. (<b>c</b>) The results of <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Θ</mo> </mrow> </semantics></math> for the ports with the top 20 annual average throughputs.</p>
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<p>Key nodes identification results using the SSHODN in GLSRFs. (<b>a</b>,<b>b</b>) The container ports with the largest changes in <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Θ</mo> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math> (circles) and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Θ</mo> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math> (stars), excluding the top 20 by annual throughput. Different colors represent different geographical regions, and the size of the shapes indicates the magnitude of <math display="inline"><semantics> <mrow> <mo>|</mo> <mo>Δ</mo> <mo>Θ</mo> <mo>|</mo> </mrow> </semantics></math>. (<b>b</b>) Dashed ellipse highlighting a zoomed-in section near Oceania. For more details, see <a href="#jmse-12-01305-t003" class="html-table">Table 3</a>.</p>
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<p>Example of second-order relationships in the ISHODN. (<b>a</b>–<b>d</b>) Nodes on either side representing paths with dependency relationships using Singapore (country) as the hub node (<math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mo>−</mo> <mi>S</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> <mi>a</mi> <mi>p</mi> <mi>o</mi> <mi>r</mi> <mi>e</mi> </mrow> </semantics></math>). The percentages on the left side of the nodes indicate the proportion of <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math> in <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math>. The percentages on the right side of the nodes represent the proportion of <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mi>r</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> <mo>−</mo> <mi>z</mi> </mrow> </semantics></math> in <math display="inline"><semantics> <mrow> <mi>n</mi> <mi>s</mi> <mi>d</mi> <mi>p</mi> <mi>h</mi> <mi>s</mi> <mi>h</mi> <mo>−</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> </mrow> </semantics></math>.</p>
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<p>Third-order and fourth-order dependency relationships in the ISHODN. (<b>a</b>,<b>b</b>) The four or five columns of nodes represent different countries. Different colors signify the extracted dependency paths, with (<b>a</b>) highlighted in blue representing <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>d</mi> <mi>p</mi> <mi>o</mi> <mo>−</mo> <mi>C</mi> <mi>h</mi> <mi>i</mi> <mi>n</mi> <mi>a</mi> </mrow> </semantics></math>.</p>
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<p>Key nodes identification results using ISHODN the GLSRF. (<b>a</b>–<b>d</b>) Yellow bars representing <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Υ</mo> </mrow> </semantics></math>, blue circles for <math display="inline"><semantics> <mo>Υ</mo> </semantics></math>, and pink stars for <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math>. Each subplot has a left y-axis showing the percentage values for <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Υ</mo> </mrow> </semantics></math> and a right y-axis for the values of <math display="inline"><semantics> <mo>Υ</mo> </semantics></math> or <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math>. (<b>a</b>) The top 10 countries or regions with the highest <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Υ</mo> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>. (<b>b</b>) The bottom 10 countries or regions with <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mo>Υ</mo> <mo>&lt;</mo> <mn>0</mn> </mrow> </semantics></math>. (<b>c</b>,<b>d</b>) Mainly Southeast Asia, Oceania, and other representative results.</p>
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<p>The evolution of <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> across various years. (<b>a</b>–<b>c</b>) Heat maps of <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> for various countries within GLSN for the years 2018, 2020, and 2023, respectively. Countries or regions colored grey indicate a <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> value of 0 for the corresponding year, meaning they were not covered in GLSRF. The intensity of the colors in the heat maps reflects the degree of dependency of the countries in GLSN, with <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> values ranging from <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>0.02</mn> <mo>]</mo> </mrow> </semantics></math>. The x-axes in (<b>d</b>,<b>e</b>) represent different years, while the y-axes show the values of <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math>. (<b>d</b>) The <math display="inline"><semantics> <mover accent="true"> <mo>Υ</mo> <mo>˜</mo> </mover> </semantics></math> values for traditionally maritime developed countries. (<b>e</b>) Data for a selection of representative countries.</p>
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<p>Key nodes identification results using the LSHODN in GLSRFs. (<b>a</b>) The geographical distribution of seven different organizations. (<b>b</b>) The results of key nodes identification, where pink represents <math display="inline"><semantics> <mo>Θ</mo> </semantics></math> and blue represents <math display="inline"><semantics> <mover accent="true"> <mo>Θ</mo> <mo>˜</mo> </mover> </semantics></math>.</p>
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24 pages, 4997 KiB  
Article
Soft Sensors for Industrial Processes Using Multi-Step-Ahead Hankel Dynamic Mode Decomposition with Control
by Luca Patanè, Francesca Sapuppo and Maria Gabriella Xibilia
Electronics 2024, 13(15), 3047; https://doi.org/10.3390/electronics13153047 - 1 Aug 2024
Viewed by 374
Abstract
In this paper, a novel data-driven approach for the development of soft sensors (SSs) for multi-step-ahead prediction of industrial process variables is proposed. This method is based on the recent developments in Koopman operator theory and dynamic mode decomposition (DMD). It is derived [...] Read more.
In this paper, a novel data-driven approach for the development of soft sensors (SSs) for multi-step-ahead prediction of industrial process variables is proposed. This method is based on the recent developments in Koopman operator theory and dynamic mode decomposition (DMD). It is derived from Hankel DMD with control (HDMDc) to deal with highly nonlinear dynamics using augmented linear models, exploiting input and output regressors. The proposed multi-step-ahead HDMDc (MSA-HDMDc) is designed to perform multi-step prediction and capture complex dynamics with a linear approximation for a highly nonlinear system. This enables the construction of SSs capable of estimating the output of a process over a long period of time and/or using the developed SSs for model predictive control purposes. Hyperparameter tuning and model order reduction are specifically designed to perform multi-step-ahead predictions. Two real-world case studies consisting of a sulfur recovery unit and a debutanizer column, which are widely used as benchmarks in the SS field, are used to validate the proposed methodology. Data covering multiple system operating points are used for identification. The proposed MSA-HDMDc outperforms currently adopted methods in the SSs domain, such as autoregressive models with exogenous inputs and finite impulse response models, and proves to be robust to the variability of systems operating points. Full article
(This article belongs to the Special Issue Nonlinear System Identification and Soft Sensor Design)
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<p>HDMDc block scheme.</p>
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<p>SRU line working scheme.</p>
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<p>Schematic representation of the debutanizer column (DC) with indication of the location of the hardware measuring devices, the model exogenous input, <span class="html-italic">u</span>, and soft sensor model output, <span class="html-italic">y</span>.</p>
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<p>SRU case study: percentage performance improvement <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>I</mi> <mo>%</mo> </mrow> </semantics></math> for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> at each prediction step, varying the input delay shifts, <math display="inline"><semantics> <msub> <mi>q</mi> <mi>u</mi> </msub> </semantics></math>, in the MSA-HDMDc algorithm. The <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>I</mi> <mo>%</mo> </mrow> </semantics></math> was calculated for each of the identified models with respect to the baseline model with <math display="inline"><semantics> <mrow> <msub> <mi>q</mi> <mi>u</mi> </msub> <mo>=</mo> <mi>q</mi> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math>.</p>
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<p>SRU case study: MSA model performances: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> for ARX, FIR, and MSA-HDMDc models by varying the reduced order, <span class="html-italic">p</span>, of the <math display="inline"><semantics> <mo>Ω</mo> </semantics></math> matrix in the <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>e</mi> </mrow> </msub> <mo>∈</mo> <mrow> <mo>{</mo> <mn>201</mn> <mo>,</mo> <mn>202</mn> <mo>,</mo> <mn>210</mn> <mo>,</mo> <mn>220</mn> <mo>,</mo> <mn>240</mn> <mo>}</mo> </mrow> </mrow> </semantics></math> and considering the matrix <math display="inline"><semantics> <msubsup> <mi>X</mi> <mi>H</mi> <mo>′</mo> </msubsup> </semantics></math> at full-order <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math>.</p>
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<p>SRU case study: barplot of <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>I</mi> <mo>%</mo> </mrow> </semantics></math> for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> with <math display="inline"><semantics> <mo>Ω</mo> </semantics></math> matrix order reduction <math display="inline"><semantics> <mrow> <msup> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>202</mn> </mrow> </semantics></math> and varying the <math display="inline"><semantics> <msup> <mi>X</mi> <mo>′</mo> </msup> </semantics></math> matrix reduction order in the range <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>e</mi> </mrow> </msub> <mo>∈</mo> <mrow> <mo>{</mo> <mn>18</mn> <mo>,</mo> <mn>20</mn> <mo>,</mo> <mn>23</mn> <mo>,</mo> <mn>25</mn> <mo>,</mo> <mn>30</mn> <mo>,</mo> <mn>35</mn> <mo>}</mo> </mrow> </mrow> </semantics></math>. The <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>I</mi> <mo>%</mo> </mrow> </semantics></math> was calculated for each of the identified models with respect to the reference model with <math display="inline"><semantics> <mrow> <msup> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>202</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math>.</p>
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<p>SRU case study: regression plots of predicted output at 30 steps versus the target measured output, <math display="inline"><semantics> <msub> <mi>y</mi> <mn>1</mn> </msub> </semantics></math>: (<b>a</b>) ARX model, (<b>b</b>) FIR model, (<b>c</b>) MSA-HDMDc model with optimal parameters <math display="inline"><semantics> <mrow> <msup> <mi>q</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>q</mi> <mi>u</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msubsup> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>202</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>r</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>25</mn> </mrow> </semantics></math>.</p>
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<p>SRU case study: comparison of the measured output (<math display="inline"><semantics> <msub> <mi>y</mi> <mn>1</mn> </msub> </semantics></math>) with the predicted ones at 30-step-ahead for the baseline and the MSA-HDMDc models with optimal parameters <math display="inline"><semantics> <mrow> <msup> <mi>q</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>q</mi> <mi>u</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msubsup> <mo>=</mo> <mn>40</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>202</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>r</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>25</mn> </mrow> </semantics></math>.</p>
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<p>SRU case study: analysis of <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math> computed using time batches of 100 samples for a 30-step-ahead prediction on a selected interval of the test dataset. The corresponding normalized input signals and associated clusters are also included. 1st panel: time evolution of the inputs, 2nd panel: input clusters, 3rd panel: time evolution of <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math>.</p>
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<p>DC case study: MSA model performances in terms of (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> for ARX, FIR and MSA-HDMDc models by varying the reduced order, <span class="html-italic">p</span>, of the <math display="inline"><semantics> <mo>Ω</mo> </semantics></math> matrix in the <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>e</mi> </mrow> </msub> <mo>∈</mo> <mrow> <mo>{</mo> <mn>65</mn> <mo>,</mo> <mn>66</mn> <mo>,</mo> <mn>70</mn> <mo>,</mo> <mn>84</mn> <mo>}</mo> </mrow> </mrow> </semantics></math> and considering the matrix <math display="inline"><semantics> <msubsup> <mi>X</mi> <mi>H</mi> <mo>′</mo> </msubsup> </semantics></math> at full-order <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>.</p>
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<p>DC case study: barplot of <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>I</mi> <mo>%</mo> </mrow> </semantics></math> for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math> with <math display="inline"><semantics> <mo>Ω</mo> </semantics></math> matrix order reduction <math display="inline"><semantics> <mrow> <msup> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>66</mn> </mrow> </semantics></math> and varying the <math display="inline"><semantics> <msup> <mi>X</mi> <mo>′</mo> </msup> </semantics></math> matrix reduction order in the range <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>e</mi> </mrow> </msub> <mo>∈</mo> <mrow> <mo>{</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>8</mn> <mo>,</mo> <mn>12</mn> <mo>}</mo> </mrow> </mrow> </semantics></math>. The <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>I</mi> <mo>%</mo> </mrow> </semantics></math> was calculated for each of the identified models with respect to the reference MSA-HDMDc model with <math display="inline"><semantics> <mrow> <msup> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>66</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>.</p>
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<p>DC case study: comparison of the measured output (<span class="html-italic">y</span>) with the predicted one at (<b>a</b>) 5-step-ahead (30 min) and (<b>b</b>) 10-step-ahead (60 min) for the baseline and the MSA-HDMDc models with the optimal parameters <math display="inline"><semantics> <mrow> <msup> <mi>q</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>q</mi> <mi>u</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msubsup> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>66</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>r</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> on a selected interval of the test dataset.</p>
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<p>DC case study: comparison of the measured output (<span class="html-italic">y</span>) with the predicted one at (<b>a</b>) 5-step-ahead (30 min) and (<b>b</b>) 10-step-ahead (60 min) for the baseline and the MSA-HDMDc models with the optimal parameters <math display="inline"><semantics> <mrow> <msup> <mi>q</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mi>q</mi> <mi>u</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msubsup> <mo>=</mo> <mn>12</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>p</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>66</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msup> <mi>r</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msup> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> on a selected interval of the test dataset.</p>
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<p>DC case study: analysis of <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math> computed using time batches of 100 samples for a 5-step-ahead prediction on a selected interval of the test dataset. The corresponding normalized input signals and associated clusters are also included. 1st panel: time evolution of the inputs, 2nd panel: input clusters, 3rd panel: time evolution of <math display="inline"><semantics> <mrow> <mi>M</mi> <mi>A</mi> <mi>P</mi> <msub> <mi>E</mi> <mo>%</mo> </msub> </mrow> </semantics></math>.</p>
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21 pages, 9889 KiB  
Article
Research on Multi-Source Data Fusion and Satellite Selection Algorithm Optimization in Tightly Coupled GNSS/INS Navigation Systems
by Xuyang Yu, Zhiming Guo and Liaoni Wu
Remote Sens. 2024, 16(15), 2804; https://doi.org/10.3390/rs16152804 - 31 Jul 2024
Viewed by 355
Abstract
With the increase in the number of Global Navigation Satellite System (GNSS) satellites and their operating frequencies, richer observation data are provided for the tightly coupled Global Navigation Satellite System/Inertial Navigation System (GNSS/INS). In this paper, we propose an efficient and robust combined [...] Read more.
With the increase in the number of Global Navigation Satellite System (GNSS) satellites and their operating frequencies, richer observation data are provided for the tightly coupled Global Navigation Satellite System/Inertial Navigation System (GNSS/INS). In this paper, we propose an efficient and robust combined navigation scheme to address the key issues of system accuracy, robustness, and computational efficiency. The tightly combined system fuses multi-source data such as the pseudo-range, the pseudo-range rate, and dual-antenna observations from the GNSS and the horizontal attitude angle from the vertical gyro (VG) in order to realize robust navigation in a sparse satellite observation environment. In addition, to cope with the high computational load faced by the system when the satellite observation conditions are good, we propose a weighted quasi-optimal satellite selection algorithm that reduces the computational burden of the navigation system by screening the observable satellites while ensuring the accuracy of the observation data. Finally, we comprehensively evaluate the proposed system through simulation experiments. The results show that, compared with the loosely coupled navigation system, our system has a significant improvement in state estimation accuracy and still provides reliable attitude estimation in regions with poor satellite observation conditions. In addition, in comparison experiments with the optimal satellite selection algorithm, our proposed satellite selection algorithm demonstrates greater advantages in terms of computational efficiency and engineering practicability. Full article
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<p>A schematic diagram of the ECEF navigation coordinate frame and body coordinate frame. The X-, Y-, and Z-axes and text within the same framework are represented in the same color.</p>
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<p>The WQOSA execution flowchart, where N represents the current total number of visible satellites, and K represents the intended number to be selected.</p>
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<p>Pictures of installed experimental equipment.</p>
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<p>(<b>a</b>) A satellite map of the vehicle’s travel trajectory and (<b>b</b>) the variation curves of observable satellites and HDOP during the experiment.</p>
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<p>Performance comparison between LC and TC schemes. (<b>a</b>) Comparison chart of attitude errors in horizontal and vertical directions. (<b>b</b>) Comparison chart of velocity errors in eastward, northward, and vertical directions.</p>
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<p>Performance comparison between LC and TC schemes. Comparison chart of positional errors in the three spatial dimensions of longitude, latitude, and altitude.</p>
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<p>Performance comparison between with VG and without VG. (<b>a</b>) Comparison chart of attitude errors in horizontal and vertical directions. (<b>b</b>) Comparison chart of velocity errors in eastward, northward, and vertical directions. (<b>c</b>) Comparison chart of positional errors in the three spatial dimensions of longitude, latitude, and altitude.</p>
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<p>Performance comparison chart of attitude errors in horizontal directions with and without VG.</p>
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<p>(<b>a</b>) The vehicle’s travel trajectory and (<b>b</b>) the variation curves of observable satellites and the GDOP during the experiment.</p>
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<p>(<b>a</b>) The GDOP variation curve under various numbers of selected satellites, where the GDOP decreases as the number of selected satellites increases. (<b>b</b>) The curve showing the variation in the average best GDOP values for each number of selected satellites.</p>
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<p>(<b>a</b>) The GDOP curves for the OSA and WQOSA satellite selection, along with the GDOP difference curve. (<b>b</b>) The variation curves of the satellite selection time consumption for the OSA and WQOSA using the experimental data.</p>
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<p>Every satellite selected in the WQOSA and QOSA has a standard deviation of the pseudo-range error (psr-std). (<b>a</b>) By taking the average of all psr-std values, we plot the mean values of psr-std over the experimental time period in the chart. (<b>b</b>) Additionally, we also plot the mean curve of the navigation error standard deviation (nav-err) for the corresponding time intervals.</p>
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11 pages, 1555 KiB  
Article
Generalized Filter Bank Orthogonal Frequency Division Multiplexing Systems for 6G
by Yu Xin, Tong Bao, Jian Hua and Hongming Zhang
Electronics 2024, 13(15), 3006; https://doi.org/10.3390/electronics13153006 - 30 Jul 2024
Viewed by 267
Abstract
In this study, generalized filter bank orthogonal frequency division multiplexing (GFB-OFDM) is proposed for 6G. In order to meet the different requirements of various scenarios in 6G, a unified structure of GFB-OFDM is designed by adopting the flexible capabilities of suitable transmission modules. [...] Read more.
In this study, generalized filter bank orthogonal frequency division multiplexing (GFB-OFDM) is proposed for 6G. In order to meet the different requirements of various scenarios in 6G, a unified structure of GFB-OFDM is designed by adopting the flexible capabilities of suitable transmission modules. In the proposed GFB-OFDM system, the coexistence of different numerologies in different sub-bands and/or the coexistence of single-carrier and multi-carrier waveforms are achieved for adjusting different scenarios in 6G. Finally, simulation results are provided to validate the BER performance of GFB-OFDM, showing that it is capable of achieving a comparable BER performance and much more flexible transmissions compared with the classic OFDM systems. Full article
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<p>Illustration of the GFB-OFDM transmitter.</p>
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<p>Illustration of the GFB-OFDM receiver.</p>
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<p>BER of GFB−OFDM with SCS = 15 kHz, compared with CP−OFDM, when communicating over AWGN channel.</p>
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<p>BER of GFB−OFDM with SCS = 15 kHz, compared with CP−OFDM, when communicating over Rayleigh channel.</p>
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<p>BER of GFB−OFDM with SCS = 30 kHz, compared with CP−OFDM, when communicating over Rayleigh channel.</p>
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<p>BER of GFB−OFDM with SCS = 60 kHz, compared with CP−OFDM, when communicating over Rayleigh channel.</p>
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<p>IFFT/FFT complexity of GFB−OFDM and CP−OFDM.</p>
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17 pages, 11064 KiB  
Article
Research on Structural Design and Optimisation Analysis of a Downhole Multi-Parameter Real-Time Monitoring System for Intelligent Well Completion
by Gang Bi, Shuaishuai Fu, Jinlong Wang, Jiemin Wu, Peijie Yuan, Xianbo Peng, Min Wang and Yongfeng Gong
Processes 2024, 12(8), 1597; https://doi.org/10.3390/pr12081597 - 30 Jul 2024
Viewed by 348
Abstract
In this paper, based on electro-hydraulic composite intelligent well-completion technology, a new type of downhole multi-parameter real-time monitoring system design scheme is established. Firstly, a multi-parameter real-time monitoring system with a special structure is designed; secondly, its reliability is analysed by applying the [...] Read more.
In this paper, based on electro-hydraulic composite intelligent well-completion technology, a new type of downhole multi-parameter real-time monitoring system design scheme is established. Firstly, a multi-parameter real-time monitoring system with a special structure is designed; secondly, its reliability is analysed by applying the method of numerical simulation; finally, in order to verify the reliability of the simulation results, a principle prototype is developed, and indoor experimental tests of fluid flow are carried out. The experimental results show that the flow rate is directly proportional to the differential pressure, and when the flow rate is certain, the higher the water content, the higher the differential pressure. The indoor experimental flow rate of 400~1000 m3/d is measured with high accuracy, and the error range is within 5%. Numerical simulation and experimental results with a high degree of fit, a flow rate of 400–1000 m3/d, the two error range within 10%, the integrated flow coefficient of the experimental value is stable between 0.75–0.815, the simulation value is stable between 0.80–0.86. The mutual verification of the two shows that the flow monitoring design meets the requirements and provides a reference basis for the structural design of the intelligent, well-completion multi-parameter real-time monitoring system. Full article
(This article belongs to the Special Issue Modeling, Control, and Optimization of Drilling Techniques)
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<p>Schematic diagram of the reverse-Venturi tube structure.</p>
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<p>Mechanical structure of a multi-parameter real-time monitoring system.</p>
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<p>Single-load stress field and displacement nephogram of monitoring bin.</p>
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<p>Combined-load stress field and displacement nephogram of monitoring bin.</p>
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<p>Sensor testing process for pressure, temperature, and water content.</p>
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<p>Structure and mesh division used for fluid simulation analysis of reverse-Venturi tubes.</p>
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<p>Simulation analysis results of fluid flow under different working conditions and water contents.</p>
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<p>The relationship between flow rate and pressure difference under different operating conditions.</p>
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<p>The relationship between flow rate and comprehensive flow coefficient under different operating conditions.</p>
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<p>Reverse-Venturi tube flow gauge structure.</p>
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<p>Reverse-Venturi flow monitoring indoor experiments.</p>
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<p>Flow measurement and errors at ambient temperature and pressure.</p>
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<p>Comparison of numerical simulation and room experiment differential pressure results.</p>
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<p>Comparison of numerical simulation and indoor experimental combined flow coefficient results.</p>
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