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25 pages, 5912 KiB  
Article
Exploration of Earth’s Magnetosphere Using CubeSats with Electric Propulsion
by Alessandro A. Quarta
Aerospace 2025, 12(3), 211; https://doi.org/10.3390/aerospace12030211 - 6 Mar 2025
Viewed by 139
Abstract
The study of the Earth’s magnetosphere through in situ observations is an important step in understanding the evolution of the Sun–Earth interaction. In this context, the long-term observation of the Earth’s magnetotail using a scientific probe in a high elliptical orbit is a [...] Read more.
The study of the Earth’s magnetosphere through in situ observations is an important step in understanding the evolution of the Sun–Earth interaction. In this context, the long-term observation of the Earth’s magnetotail using a scientific probe in a high elliptical orbit is a challenging mission scenario due to the alignment of the magnetotail direction with the Sun–Earth line, which requires a continuous rotation of the apse line of the spacecraft’s geocentric orbit. This aspect makes the mission scenario particularly suitable for space vehicles equipped with propellantless propulsion systems, such as the classic solar sails which convert the solar radiation pressure into propulsive acceleration without propellant expenditure. However, a continuous rotation of the apse line of the osculating orbit can be achieved using a more conventional solar electric thruster, which introduces an additional constraint on the duration of the scientific mission due to the finite mass of the propellant stored on board the spacecraft. This paper analyzes the potential of a typical CubeSat equipped with a commercial miniaturized electric thruster in performing the rotation of the apse line of a geocentric orbit suitable for the in situ observation of the Earth’s magnetotail. The paper also analyzes the impact of the size of a thruster array on the flight performance for an assigned value of the payload mass and the science orbit’s characteristics. In particular, this work illustrates the optimal guidance laws that allow us to maximize the duration of the scientific mission for an assigned CubeSat’s configuration. In this sense, this paper expands the literature regarding the study of this interesting mission scenario by extending the study to conventional propulsion systems that use a propellant to provide a continuous and steerable thrust vector. Full article
(This article belongs to the Section Astronautics & Space Science)
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<p>System layout of BIT-3 (gimbaled) engine unit with integrated propellant tank, which contains <math display="inline"><semantics> <mrow> <mn>1.5</mn> <mspace width="0.166667em"/> <mi>kg</mi> </mrow> </semantics></math> of solid iodine. Image courtesy of Busek Co. Inc.</p>
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<p>Mass distribution of the nine possible CubeSat configurations as a function of <span class="html-italic">N</span> and <span class="html-italic">n</span>. (<b>a</b>) Case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>; (<b>c</b>) case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>CubeSat’s mass breakdown when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>∈</mo> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>}</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mi>N</mi> <mo>}</mo> </mrow> </semantics></math>. (<b>a</b>) Case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>; (<b>b</b>) case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>c</b>) case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>; (<b>d</b>) case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>; (<b>e</b>) case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>; (<b>f</b>) case of <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>CubeSat science orbit (<math display="inline"><semantics> <mrow> <mn>11</mn> <mspace width="0.166667em"/> <msub> <mi>R</mi> <mo>⊕</mo> </msub> <mo>×</mo> <mn>23</mn> <mspace width="0.166667em"/> <msub> <mi>R</mi> <mo>⊕</mo> </msub> </mrow> </semantics></math> geocentric ellipse) for the observation of the Earth’s magnetotail.</p>
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<p>Conceptual scheme of the rotation of the science orbit.</p>
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<p>Mission lifetime as a percentage of the target value of <math display="inline"><semantics> <mrow> <mn>2</mn> <mspace width="0.166667em"/> <mi>years</mi> </mrow> </semantics></math>.</p>
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<p>CubeSat trajectory when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>}</mo> </mrow> </semantics></math>. Blue circle → Earth; red dot → starting point which coincides with initial perigee.</p>
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<p>CubeSat trajectory when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>∈</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mn>3</mn> <mo>}</mo> </mrow> </semantics></math>. Blue circle → Earth; red dot → starting point which coincides with initial perigee.</p>
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<p>Time variation of the orbital elements of the CubeSat’s osculating orbit when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>. Red dot → starting point.</p>
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<p>Time variation of <math display="inline"><semantics> <mi>ω</mi> </semantics></math> and the angular position of the Sun–Earth line given by <math display="inline"><semantics> <mrow> <msub> <mo>Ω</mo> <mo>⊕</mo> </msub> <mspace width="0.166667em"/> <mi>t</mi> </mrow> </semantics></math>, when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>.</p>
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<p>Variation in <math display="inline"><semantics> <mrow> <mo>{</mo> <mi>a</mi> <mo>,</mo> <mi>e</mi> <mo>,</mo> <mi>ω</mi> <mo>}</mo> </mrow> </semantics></math> along the first reduced interval <math display="inline"><semantics> <mrow> <mi>ν</mi> <mo>∈</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>2</mn> <mi>π</mi> <mo>]</mo> <mspace width="0.166667em"/> <mi>rad</mi> </mrow> </semantics></math> when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>. Red dot → starting point; red dashed line →<math display="inline"><semantics> <mrow> <msub> <mo>Ω</mo> <mo>⊕</mo> </msub> <mspace width="0.166667em"/> <mi>t</mi> </mrow> </semantics></math>.</p>
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<p>Variation with <math display="inline"><semantics> <mi>ν</mi> </semantics></math> of the two control terms along the first reduced interval when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>. Red dot → starting point.</p>
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<p>Variation with <math display="inline"><semantics> <mi>ν</mi> </semantics></math> (or <span class="html-italic">t</span>) of the CubeSat’s total mass during the first reduced interval, when <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>=</mo> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>. Red dot → starting point.</p>
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23 pages, 9774 KiB  
Article
Predictive Torque Control of Permanent Magnet Motor for New-Energy Vehicles Under Low-Carrier-Ratio Conditions
by Zhiqiang Wang, Zhichen Lin, Xuefeng Jin and Yan Yan
World Electr. Veh. J. 2025, 16(3), 146; https://doi.org/10.3390/wevj16030146 - 4 Mar 2025
Viewed by 184
Abstract
The model predictive-torque-control strategy of a permanent magnet synchronous motor (PMSM) has many advantages such as a fast dynamic response and the ease of implementation. However, when the permanent magnet motor has a large number of pole pairs or operates at high-speed, due [...] Read more.
The model predictive-torque-control strategy of a permanent magnet synchronous motor (PMSM) has many advantages such as a fast dynamic response and the ease of implementation. However, when the permanent magnet motor has a large number of pole pairs or operates at high-speed, due to constraints such as the inverter switching frequency, sampling time, and algorithm execution time, the motor carrier ratio (the ratio of control frequency to operating frequency) becomes relatively low. The discrete model derived from and based on the forward Euler method has a large model error when the carrier ratio decreases, which leads to voltage vector misjudgment and inaccurate duty cycle calculation, thus leading to the decline of control performance. Meanwhile, the shortcomings of the traditional model predictive-torque-control strategy limit the steady-state performance. In response to the above issues, this paper proposes an improved model predictive-torque-control strategy suitable for low-carrier-ratio conditions. The strategy consists of an improved discrete model that considers rotor-angle-position variations and a model prediction algorithm. It also analyzes the sensitivity of model predictive control to parameter changes and designs an online parameter optimization algorithm. Compared with the traditional forward Euler method, the improved discrete model proposed in this paper has obvious advantages under low-carrier-ratio conditions; at the same time, the parameter optimization process enhances the parameter robustness of the model prediction algorithm. Moreover, the proposed model predictive-torque-control strategy has high torque tracking accuracy. The experimental results verify the feasibility and effectiveness of the proposed strategy. Full article
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<p>The block diagram of traditional model predictive torque control.</p>
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<p>The block diagram of vector action within a unit carrier period.</p>
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<p>The plot of torque trajectories for different vector combinations.</p>
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<p>The block diagram of the optimal vector action combination.</p>
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<p>The comparison chart of action vectors, three-phase switching states, and torque fluctuations per unit carrier period with the improved sampling and duty cycle update strategy.</p>
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<p>The flow chart of the model reference adaptive-parameter-optimization algorithm.</p>
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<p>General block diagram of the control strategy proposed in this paper.</p>
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<p>The comparison waveforms of the current, stator flux, and torque of the predictive model at low speed.</p>
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<p>The comparison waveforms of the current, stator flux, and torque of the predictive model at medium speed.</p>
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<p>The improved prediction model current, stator flux, and torque waveform at high speed.</p>
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<p>The waveform of parameter optimization link current, stator flux, and torque.</p>
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<p>The comparison of difference in E before and after optimization.</p>
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<p>The current THD analysis of parameter normal, parameter mismatch, and optimization completion.</p>
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<p>The plot of model predictive-torque-control strategy current, stator flux and torque waveforms at low speed.</p>
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<p>The plot of model predictive-torque-control strategy current, stator flux, and torque waveforms at medium speed.</p>
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<p>The plot of model predictive-torque-control strategy current, stator flux and torque waveforms at high speed.</p>
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29 pages, 10206 KiB  
Article
Finite-Time Control for Satellite Formation Reconfiguration and Maintenance in LEO: A Nonlinear Lyapunov-Based SDDRE Approach
by Majid Bakhtiari, Amirhossein Panahyazdan and Ehsan Abbasali
Aerospace 2025, 12(3), 201; https://doi.org/10.3390/aerospace12030201 - 28 Feb 2025
Viewed by 331
Abstract
This paper introduces a nonlinear Lyapunov-based Finite-Time State-Dependent Differential Riccati Equation (FT-SDDRE) control scheme, considering actuator saturation constraints and ensuring that the control system operates within safe operational limits designed for satellite reconfiguration and formation-keeping in low Earth orbit (LEO) missions. This control [...] Read more.
This paper introduces a nonlinear Lyapunov-based Finite-Time State-Dependent Differential Riccati Equation (FT-SDDRE) control scheme, considering actuator saturation constraints and ensuring that the control system operates within safe operational limits designed for satellite reconfiguration and formation-keeping in low Earth orbit (LEO) missions. This control approach addresses the challenges of reaching the relative position and velocity vectors within a defined timeframe amid various orbital perturbations. The proposed approach guarantees precise formation control by utilizing a high-fidelity relative motion model that incorporates all zonal harmonics and atmospheric drag, which are the primary environmental disturbances in LEO. Additionally, the article presents an optimization methodology to determine the most efficient State-Dependent Coefficient (SDC) form regarding fuel consumption. This optimization process minimizes energy usage through a hybrid genetic algorithm and simulated annealing (HGASA), resulting in improved performance. In addition, this paper includes a sensitivity analysis to identify the optimized SDC parameterization for different satellite reconfiguration maneuvers. These maneuvers encompass radial, along-track, and cross-track adjustments, each with varying baseline distances. The analysis provides insights into how different parameterizations affect reconfiguration performance, ensuring precise and efficient control for each type of maneuver. The finite-time controller proposed here is benchmarked against other forms of SDRE controllers, showing reduced error margins. To further assess the control system’s effectiveness, an input saturation constraint is integrated, ensuring that the control system operates within safe operational limits, ultimately leading to the successful execution of the mission. Full article
(This article belongs to the Section Astronautics & Space Science)
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<p>Schematic diagram of ECI and LVLH frames used in relative motion analysis.</p>
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<p>Schematic diagram of the deputy satellite relative to the target satellite.</p>
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<p>The 3D sketch of deputy satellite trajectory in LVLH frame.</p>
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<p>The introduced model’s position accuracy compared to the ERM Model.</p>
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<p>The introduced model’s velocity accuracy compared to the ERM Model.</p>
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<p>The variation in the optimal values of <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>γ</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>δ</mi> </mrow> </semantics></math> in the scenarios with radial motion only (<b>a</b>), along-track motion only (<b>b</b>), and cross-track motion only (<b>c</b>).</p>
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<p>Block diagram of the satellite formation flying control and optimization process.</p>
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<p>Uncontrolled motion of deputy satellites with respect to the target satellite.</p>
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<p>The process of cost reduction in optimization through the HGASA.</p>
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<p>The absolute sum of the magnitudes of the control forces for four deputy satellites using three types of SDC and the optimized form.</p>
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<p>The 3D sketch of deputy satellites’ formation reconfiguration and maintenance trajectory utilizing the Lyapunov-based FT-SDDRE method (In this figure, The filled circles indicate the deputy satellites’ initial positions, while the hollow circles represent their positions at the end of the mission).</p>
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<p>The 2D sketch of deputy satellites’ formation reconfiguration and maintenance trajectory utilizing the Lyapunov-based FT-SDDRE method in different perspectives (In this figure, The filled circles indicate the deputy satellites’ initial positions, while the hollow circles represent their positions at the end of the mission).</p>
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<p>The position tracking of deputy satellites utilizing the Lyapunov-based FT-SDDRE method.</p>
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<p>The velocity tracking of deputy satellites utilizing the Lyapunov-based SDDRE method.</p>
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<p>The relative distance among deputy satellites in the projected circular orbit formation after utilizing the Lyapunov-based FT-SDDRE method.</p>
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<p>The relative distance among deputy satellites in <math display="inline"><semantics> <mrow> <mi>y</mi> <mo>−</mo> <mi>z</mi> </mrow> </semantics></math> plane in the projected circular orbit formation after utilizing the Lyapunov-based FT-SDDRE method.</p>
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<p>The absolute position tracking error of the Lyapunov-based FT-SDDRE method compared to the classical SDRE and finite-time STM approach by deputy satellites.</p>
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<p>The absolute velocity tracking error of the Lyapunov-based FT-SDDRE method compared to the classical SDRE and finite-time STM approach by deputy satellites.</p>
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<p>The control force generated by Lyapunov-based FT-SDDRE controller for deputy satellites.</p>
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16 pages, 287 KiB  
Article
Bi-Objective Optimization for Transportation: Generating Near-Optimal Subsets of Pareto Optimal Solutions
by Hongyu Zhang, Qingfang Ruan, Yong Jin and Shuaian Wang
Appl. Sci. 2025, 15(5), 2519; https://doi.org/10.3390/app15052519 - 26 Feb 2025
Viewed by 217
Abstract
Bi-objective optimization seeks to obtain Pareto optimal solutions that balance two trade-off objectives, providing guidance for decision making in various fields, particularly in the field of transportation. The novelty of this study lies in two aspects. On the one hand, considering that Pareto [...] Read more.
Bi-objective optimization seeks to obtain Pareto optimal solutions that balance two trade-off objectives, providing guidance for decision making in various fields, particularly in the field of transportation. The novelty of this study lies in two aspects. On the one hand, considering that Pareto optimal solutions are often numerous, finding the full set of Pareto optimal solutions is often computationally challenging and unnecessary for practical purposes. Therefore, we shift the focus of bi-objective optimization to finding a subset of Pareto optimal solutions whose resulting set of nondominated objective vectors is the same as, or at least a good approximation of, the full set of nondominated objective vectors for the problem. In particular, we elaborate three methods for generating a near-optimal subset of Pareto optimal solutions, including the revised ϵ-constraint method, the improved revised ϵ-constraint method, and the augmented ϵ-constraint method. More importantly, the near-optimality of the Pareto optimal solution subset obtained by these methods is rigorously analyzed and proved from a mathematical point of view. This study helps to offer theoretical support for future studies to find the subset of Pareto optimal solutions, which reduces the unnecessary workload and improves the efficiency of solving bi-objective optimization problems while guaranteeing a pre-specified tolerance level. Full article
(This article belongs to the Special Issue Advanced, Smart, and Sustainable Transportation)
16 pages, 5435 KiB  
Article
PAPRec: 3D Point Cloud Reconstruction Based on Prior-Guided Adaptive Probabilistic Network
by Caixia Liu, Minhong Zhu, Yali Chen, Xiulan Wei and Haisheng Li
Sensors 2025, 25(5), 1354; https://doi.org/10.3390/s25051354 - 22 Feb 2025
Viewed by 354
Abstract
Inferring a complete 3D shape from a single-view image is an ill-posed problem. The proposed methods often have problems such as insufficient feature expression, unstable training and limited constraints, resulting in a low accuracy and ambiguity reconstruction. To address these problems, we propose [...] Read more.
Inferring a complete 3D shape from a single-view image is an ill-posed problem. The proposed methods often have problems such as insufficient feature expression, unstable training and limited constraints, resulting in a low accuracy and ambiguity reconstruction. To address these problems, we propose a prior-guided adaptive probabilistic network for single-view 3D reconstruction, called PAPRec. In the training stage, PAPRec encodes a single-view image and its corresponding 3D prior into image feature distribution and point cloud feature distribution, respectively. PAPRec then utilizes a latent normalizing flow to fit the two distributions and obtains a latent vector with rich cues. PAPRec finally introduces an adaptive probabilistic network consisting of a shape normalizing flow and a diffusion model in order to decode the latent vector as a complete 3D point cloud. Unlike the proposed methods, PAPRec fully learns the global and local features of objects by innovatively integrating 3D prior guidance and the adaptive probability network under the optimization of a loss function combining prior, flow and diffusion losses. The experimental results on the public ShapeNet dataset show that PAPRec, on average, improves CD by 2.62%, EMD by 5.99% and F1 by 4.41%, in comparison to several state-of-the-art methods. Full article
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<p>The architecture of our proposed PAPRec. In the training stage, PAPRec encodes a single-view image and its corresponding 3D shape into feature distributions. PAPRec then utilizes a latent normalizing flow to fit the distributions and obtain a shape latent vector. PAPRec finally introduces an adaptive probabilistic network, which consists of a flow model and a diffusion model for fully learning the global and local features of objects, to decode the latent vector as a complete 3D point cloud. In the testing stage, PAPRec utilizes the trained image encoder, latent normalizing flow and adaptive decoder to reconstruct the 3D point cloud from a single-view image.</p>
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<p>The qualitative comparison results of different autoencoders. Our reconstructed chairs and airplanes exhibit higher accuracy, while the reconstructed tables and lamps are more complete. This clearly demonstrates that PAPRec has greater effectiveness and a stronger capacity to represent diverse shapes.</p>
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<p>The qualitative comparison results of the single-view reconstruction methods. Our reconstructed monitors, benches and cars exhibit more details, while the reconstructed tables, planes and chairs are more accurate. This clearly demonstrates that PAPRec has better robustness.</p>
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<p>The qualitative comparison results of ablation study. ‘-Prior’, ‘-Flow’ and ‘-Diffusion’ denote PAPRec without the point cloud learning, the shape normalizing flow and the diffusion model, respectively. ‘Fixed decoder’ denotes PAPRec adopts fixed weights in the decoder. The full model achieves superior performance in handling noise and reproducing details.</p>
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31 pages, 4303 KiB  
Article
Research on Flexible Job Shop Scheduling Method for Agricultural Equipment Considering Multi-Resource Constraints
by Zhangliang Wei, Zipeng Yu, Renzhong Niu, Qilong Zhao and Zhigang Li
Agriculture 2025, 15(4), 442; https://doi.org/10.3390/agriculture15040442 - 19 Feb 2025
Viewed by 247
Abstract
The agricultural equipment market has the characteristics of rapid demand changes and high demand for machine models, etc., so multi-variety, small-batch, and customized production methods have become the mainstream of agricultural machinery enterprises. The flexible job shop scheduling problem (FJSP) in the context [...] Read more.
The agricultural equipment market has the characteristics of rapid demand changes and high demand for machine models, etc., so multi-variety, small-batch, and customized production methods have become the mainstream of agricultural machinery enterprises. The flexible job shop scheduling problem (FJSP) in the context of agricultural machinery and equipment manufacturing is addressed, which involves multiple resources including machines, workers, and automated guided vehicles (AGVs). The aim is to optimize two objectives: makespan and the maximum continuous working hours of all workers. To tackle this complex problem, a Multi-Objective Discrete Grey Wolf Optimization (MODGWO) algorithm is proposed. The MODGWO algorithm integrates a hybrid initialization strategy and a multi-neighborhood local search to effectively balance the exploration and exploitation capabilities. An encoding/decoding method and a method for initializing a mixed population are introduced, which includes an operation sequence vector, machine selection vector, worker selection vector, and AGV selection vector. The solution-updating mechanism is also designed to be discrete. The performance of the MODGWO algorithm is evaluated through comprehensive experiments using an extended version of the classic Brandimarte test case by randomly adding worker and AGV information. The experimental results demonstrate that MODGWO achieves better performance in identifying high-quality solutions compared to other competitive algorithms, especially for medium- and large-scale cases. The proposed algorithm contributes to the research on flexible job shop scheduling under multi-resource constraints, providing a novel solution approach that comprehensively considers both workers and AGVs. The research findings have practical implications for improving production efficiency and balancing multiple objectives in agricultural machinery and equipment manufacturing enterprises. Full article
(This article belongs to the Section Agricultural Technology)
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<p>A simple example of the FJSP with workers and AGVs.</p>
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<p>GWO hierarchical categories.</p>
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<p>Individual encoding example: (<b>a</b>) OS vector, (<b>b</b>) MS vector, (<b>c</b>) WS vector, and (<b>d</b>) AS vector.</p>
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<p>Updating mechanism for operation sequencing.</p>
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<p>Updating mechanism for machine selection and AGV selection.</p>
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<p>VNS1 neighborhood search process.</p>
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<p>VNS2 neighborhood search process.</p>
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<p>VNS3 neighborhood search process.</p>
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<p>VNS4 neighborhood search process.</p>
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<p>Box plots for (<b>a</b>) IGD metric and (<b>b</b>) HV metric from <a href="#agriculture-15-00442-t005" class="html-table">Table 5</a>.</p>
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<p>Comparison of performance of algorithms on small-scale instances based on (<b>a</b>) IGD; (<b>b</b>) HV.</p>
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<p>Comparison of performance of algorithms on medium scale instances based on (<b>a</b>) IGD; (<b>b</b>) HV.</p>
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<p>Comparison of performance of algorithms on large-scale instances based on (<b>a</b>) IGD; (<b>b</b>) HV.</p>
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<p>Scheduling Gantt chart of MK05_3_4.</p>
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<p>Gantt charts of two scheduling schemes: (<b>a</b>) single-objective scheduling considering only makespan from the perspective of workers; (<b>b</b>) dual-objective scheduling considering the continuous working hours of workers from the perspective of workers.</p>
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<p>Distribution diagram of Pareto solutions.</p>
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24 pages, 1668 KiB  
Article
Robust Sidelobe Control for Adaptive Beamformers Against Array Imperfections via Subspace Approximation-Based Optimization
by Yang Zou, Zhoupeng Ding, Hongtao Li, Shengyao Chen, Sirui Tian and Jin He
Remote Sens. 2025, 17(4), 697; https://doi.org/10.3390/rs17040697 - 18 Feb 2025
Viewed by 136
Abstract
Conventional adaptive beamformers usually suffer from serious performance degradation when the receive array is imperfect and unknown sporadic interferences appear. To enhance robustness against array imperfections and simultaneously suppress sporadic interferences, this paper studies robust adaptive beamforming (RAB) with accurate sidelobe level (SLL) [...] Read more.
Conventional adaptive beamformers usually suffer from serious performance degradation when the receive array is imperfect and unknown sporadic interferences appear. To enhance robustness against array imperfections and simultaneously suppress sporadic interferences, this paper studies robust adaptive beamforming (RAB) with accurate sidelobe level (SLL) control, where the imperfect array steering vector (SV) is expressed as a spherical uncertainty set. Under the maximum signal-to-interference-plus-noise ratio (SINR) criterion and robust SLL constraints, we formulate the resultant RAB into a second-order cone programming problem, which is computationally prohibitive due to numerous robust quadratic SLL constraints. To tackle this issue, we provide a subspace approximation-based method to approximate the whole sidelobe space, thus replacing all robust SLL constraints with a single subspace constraint. Moreover, we leverage the Gauss–Legendre quadrature-based scheme to generate the sidelobe space in a computationally efficient manner. Additionally, we give an explicit approach for determining the norm upper bound of SV uncertainty sets under various imperfection scenarios, addressing the challenge of obtaining this upper bound in practice.Simulation results showed that the proposed subspace approximation-based RAB beamformer had a better SINR performance than typical counterparts and was much more computationally efficient. Full article
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<p>The impact of numerical integration methods on the SV approximation error with different SLL control factors. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ϑ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>ϑ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mrow> <mrow> <mo>|</mo> <mi>ϑ</mi> <mo>−</mo> </mrow> <msub> <mi>ϑ</mi> <mn>0</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </mrow> </semantics></math>.</p>
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<p>The impact of the selected subspace dimension on the SV approximation error with different SLL control factors. (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>ϑ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>ϑ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mrow> <mrow> <mo>|</mo> <mi>ϑ</mi> <mo>−</mo> </mrow> <msub> <mi>ϑ</mi> <mn>0</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </mrow> </semantics></math>.</p>
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<p>The performance of the output SINR with exactly known SVs versus SNR under varying orders of GLQ and dimensions of subspace.</p>
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<p>The impact of the preset norm upper bound of uncertainty sets on beamforming performance. (<b>a</b>) Output SINR, (<b>b</b>) PSL.</p>
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<p>The performance of all RAB methods with exactly known SVs. (<b>a</b>) Output SINR versus SNR with <math display="inline"><semantics> <mrow> <mi>INR</mi> <mo>=</mo> <mn>30</mn> <mspace width="4.pt"/> <mi>dB</mi> </mrow> </semantics></math>, (<b>b</b>) Receive beampatterns with <math display="inline"><semantics> <mrow> <mi>SNR</mi> <mo>=</mo> <mn>20</mn> <mspace width="4.pt"/> <mi>dB</mi> </mrow> </semantics></math>.</p>
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<p>The performance of all RAB methods with random and bounded SV mismatches. (<b>a</b>) Output SINR versus SNR with <math display="inline"><semantics> <mrow> <mi>INR</mi> <mo>=</mo> <mn>30</mn> <mspace width="4.pt"/> <mi>dB</mi> </mrow> </semantics></math>, (<b>b</b>) Received beampatterns with <math display="inline"><semantics> <mrow> <mi>SNR</mi> <mo>=</mo> <mn>20</mn> <mspace width="4.pt"/> <mi>dB</mi> </mrow> </semantics></math>.</p>
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<p>The output SINR performance of all RAB methods with SV mismatches yielded with different practical factors. (<b>a</b>) Array geometry error, (<b>b</b>) channel gain-phase errors, (<b>c</b>) wavefront distortion.</p>
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<p>The SINR performance of all RAB methods with unknown sporadic interferences appearing in the sidelobe region. (<b>a</b>) Output SINR versus SNR in the independent interference scenario, (<b>b</b>) output SINR versus the INR of the independent sporadic interferences, (<b>c</b>) output SINR versus SNR in the multipath interference scenario, (<b>d</b>) output SINR versus the INR of multipath sporadic interferences.</p>
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<p>Consumed CPU time of the proposed and the directly solving (12) methods.</p>
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21 pages, 783 KiB  
Article
Robust Beamfocusing for Secure NFC with Imperfect CSI
by Weijian Chen, Zhiqiang Wei and Zai Yang
Sensors 2025, 25(4), 1240; https://doi.org/10.3390/s25041240 - 18 Feb 2025
Viewed by 238
Abstract
In this paper, we consider the issue of the physical layer security (PLS) problem between two nodes, i.e., transmitter (Alice) and receiver (Bob), in the presence of an eavesdropper (Eve) in a near-field communication (NFC) system. Notably, massive multiple-input multiple-output (MIMO) arrays significantly [...] Read more.
In this paper, we consider the issue of the physical layer security (PLS) problem between two nodes, i.e., transmitter (Alice) and receiver (Bob), in the presence of an eavesdropper (Eve) in a near-field communication (NFC) system. Notably, massive multiple-input multiple-output (MIMO) arrays significantly increase array aperture, thereby rendering the eavesdroppers more inclined to lurk near the transmission end. This situation necessitates using near-field channel models to more accurately describe channel characteristics. We consider two schemes with imperfect channel estimation information (CSI). The first scheme involves a conventional multiple-input multiple-output multiple-antenna eavesdropper (MIMOME) setup, where Alice simultaneously transmits information signal and artificial noise (AN). In the second scheme, Bob operates in a full-duplex (FD) mode, with Alice transmitting information signal while Bob emits AN. We then jointly design beamforming and AN vectors to degrade the reception signal quality at Eve, based on the signal-to-interference-plus-noise ratio (SINR) of each node. To tackle the power minimization problem, we propose an iterative algorithm that includes an additional constraint to ensure adherence to specified quality-of-service (QoS) metrics. Additionally, we decompose the robust optimization problem of the two schemes into two sub-problems, with one that can be solved using generalized Rayleigh quotient methods and the other that can be addressed through semi-definite programming (SDP). Finally, our simulation results confirm the viability of the proposed approach and demonstrate the effectiveness of the protection zone for NFC systems operating with CSI. Full article
(This article belongs to the Special Issue Secure Communication for Next-Generation Wireless Networks)
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<p>The near-field secure wireless communication system.</p>
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<p>Convergence behavior of the proposed algorithm for both schemes. (<b>a</b>) When Eve is within the near-field region of Alice. (<b>b</b>) When Eve is within the near-field region of Bob.</p>
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<p>The average transmit power versus minimum required SINR <math display="inline"><semantics> <msub> <mo>Γ</mo> <mi>Req</mi> </msub> </semantics></math>.</p>
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<p>(<b>a</b>) The average transmit power versus number of Alice’s antennas <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">A</mi> </msub> </semantics></math>. (<b>b</b>) The average transmit power versus number of Eve’s antennas <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">E</mi> </msub> </semantics></math>.</p>
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<p>The average transmit power versus the distance between Alice and Eve.</p>
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<p>Normalized power heat maps for Scheme I. (<b>a</b>) Desired signal power. (<b>b</b>) Interference-plus-noise power.</p>
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<p>Normalized power heat maps for scheme II. (<b>a</b>) Desired signal power. (<b>b</b>) Interference-plus-noise power.</p>
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23 pages, 6635 KiB  
Article
Data-Driven Modeling of Electric Vehicle Charging Sessions Based on Machine Learning Techniques
by Raymond O. Kene and Thomas O. Olwal
World Electr. Veh. J. 2025, 16(2), 107; https://doi.org/10.3390/wevj16020107 - 16 Feb 2025
Viewed by 323
Abstract
The increased demand for electricity is inevitable due to transport sector electrification. A major part of this demand is from electric vehicle (EV) charging on a large scale, which is now a growing concern for the grid power distribution system. The lack of [...] Read more.
The increased demand for electricity is inevitable due to transport sector electrification. A major part of this demand is from electric vehicle (EV) charging on a large scale, which is now a growing concern for the grid power distribution system. The lack of insight into grid energy demand by EVs makes it difficult to manage these consumptions on a large scale. For any grid load management application to be effective in minimizing the impact of uncontrolled charging, there is a need to gain insight into EV energy demand. To address this issue, this study presents data-driven modeling of EV charging sessions based on machine learning (ML) techniques. The purpose of using ML as an approach is to provide insight for estimating future energy demand and minimizing the impact of EV charging on the grid. To achieve the aim of this study, firstly, we investigated the impact of large-scale charging of EVs on the grid. Based on this, we formulated an objective function, expressed as a sum of utility functions when EVs charge on the grid with constraints imposed on voltage levels and charging power. Secondly, we employed a graphical modeling approach to study the temporal distribution of EV energy consumption based on real-world datasets from EV charging sessions. Thirdly, using ML regression models, we predicted EV energy consumption using four different models of fine tree, linear regression, linear SVM (support vector machine), and neural network. We used 5-fold cross-validation to protect against overfitting and evaluated the performances of these models using regression analysis metrics. The results from our predictions showed better accuracy when compared with the results from the work of other authors. Full article
(This article belongs to the Special Issue Data Exchange between Vehicle and Power System for Optimal Charging)
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<p>Graphical framework of system model and study workflow.</p>
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<p>Modified IEEE 33-bus network single-line diagram with EV charging.</p>
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<p>Energy outlook: cumulative sum of EV energy consumption (kWh).</p>
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<p>Temporal distributions of EV energy consumption profiles January–December 2022.</p>
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<p>Average state of charge for all EVs before charging on the grid.</p>
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<p>Fine tree predictions of EV energy consumption.</p>
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<p>Linear regression predictions of EV energy consumption.</p>
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<p>Linear SVM predictions of EV energy consumption.</p>
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<p>Neural network predictions of EV energy consumption.</p>
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16 pages, 335 KiB  
Article
Beamforming for the Cooperative Non-Orthogonal Multiple Access Transmission with Full-Duplex Relaying with Application to Security Attack
by Duckdong Hwang, Sung Sik Nam, Janghoon Yang and Hyoung-Kyu Song
Sensors 2025, 25(4), 1172; https://doi.org/10.3390/s25041172 - 14 Feb 2025
Viewed by 596
Abstract
We investigate the cooperative non-orthogonal multiple access (CNOMA) transmission through a full-duplex (FD) decode-and-forward (DaF) mode relay and propose two sub-optimal beamforming schemes for this CNOMA FD relay channel. For the optimization metric, we use the end-to-end information rate based on the mutual [...] Read more.
We investigate the cooperative non-orthogonal multiple access (CNOMA) transmission through a full-duplex (FD) decode-and-forward (DaF) mode relay and propose two sub-optimal beamforming schemes for this CNOMA FD relay channel. For the optimization metric, we use the end-to-end information rate based on the mutual information from information theory. In addition to the pure CNOMA relay channel, the proposed beamforming schemes are applied to the security attack case as well, where an unauthorized eavesdropper tries to overhear the CNOMA transmission. The FD operation incurs the self-interference (SI) at the relay and the DaF mode along with CNOMA transmission forces the weakest link among the links toward three involved nodes to determine the end-to-end throughput. These facts lay the foundation for the designing and optimization of the beamforming vectors at the access point (AP) and at the relay. The first proposed sub-optimal optimization algorithm for the beamformer relies on the quadratically constrained quadratic problem (QCQP) in its central part, and this OCQP is iteratively applied with different interference level values at the near CNOMA user as the constraint term until some conditions for the design objectives are met. In addition to the first algorithm, a zero-forcing-based beamforming algorithm is proposed for a reference scheme. The proposed two algorithms are slightly modified to address the security-attacked CNOMA FD relay channel when a illegal user overhears the legitimate transmission. Simulation results are presented to advocate for the efficiency of the proposed algorithms for the CNOMA channel both with and without a security attack from an eavesdropper. Full article
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<p>Cooperative Non-Orthogonal Multiple Access Transmission system through an FDR with 2 user terminals under security attack from the eavesdropper (Eve). The FDR operates in the DaF protocol. The AP and the FDR have multiple antennas while the two user terminals and Eve are equipped with single antennas, respectively. The direct channel from the AP to the far user (<math display="inline"><semantics> <msub> <mi>U</mi> <mn>2</mn> </msub> </semantics></math>) is blocked unlike the near user (<math display="inline"><semantics> <msub> <mi>U</mi> <mn>1</mn> </msub> </semantics></math>) case.</p>
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<p>Comparison of the sum rate <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>S</mi> <mi>R</mi> </mrow> </msub> </semantics></math> of the proposed algorithms for the FDR CNOMA channel against the source transmit power with different <math display="inline"><semantics> <msub> <mi>α</mi> <mi>R</mi> </msub> </semantics></math> values when <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msub> <mi>N</mi> <mi>r</mi> </msub> <mo>=</mo> <msub> <mi>N</mi> <mi>t</mi> </msub> <mo>=</mo> <mn>3</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>42</mn> <mspace width="4pt"/> <mrow> <mo>(</mo> <mi>dB</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>5</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>. The path-loss from the FDR to users <math display="inline"><semantics> <msub> <mi>α</mi> <mi>U</mi> </msub> </semantics></math> is set to <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>100</mn> </mrow> </semantics></math> to scale the big <math display="inline"><semantics> <msub> <mi>P</mi> <mi>r</mi> </msub> </semantics></math> values down to realistic levels at users since the <math display="inline"><semantics> <msub> <mi>P</mi> <mi>r</mi> </msub> </semantics></math> values are taken to reflect strong SI power after the analogue SI cancellation.</p>
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<p>Comparison of the sum rate <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>S</mi> <mi>R</mi> </mrow> </msub> </semantics></math> of the proposed algorithms for the FDR CNOMA channel against the FDR transmit power with different <math display="inline"><semantics> <msub> <mi>α</mi> <mi>R</mi> </msub> </semantics></math> values when <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msub> <mi>N</mi> <mi>r</mi> </msub> <mo>=</mo> <msub> <mi>N</mi> <mi>t</mi> </msub> <mo>=</mo> <mn>3</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>15</mn> <mspace width="4pt"/> <mrow> <mo>(</mo> <mi>dB</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>5</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>. The path-loss from the FDR to users <math display="inline"><semantics> <msub> <mi>α</mi> <mi>U</mi> </msub> </semantics></math> is set to <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>100</mn> </mrow> </semantics></math>.</p>
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<p>Comparison of the sum rate <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>S</mi> <mi>R</mi> </mrow> </msub> </semantics></math> of the proposed algorithms for the FDR CNOMA channel against the number of FDR transmit antennas <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>N</mi> <mi>r</mi> </msub> </mrow> </semantics></math> with different <math display="inline"><semantics> <msub> <mi>α</mi> <mi>R</mi> </msub> </semantics></math> values when <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mspace width="4pt"/> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>42</mn> <mspace width="4pt"/> <mrow> <mo>(</mo> <mi>dB</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>15</mn> <mspace width="4pt"/> <mrow> <mo>(</mo> <mi>dB</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>5</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>. The path-loss from the FDR to users <math display="inline"><semantics> <msub> <mi>α</mi> <mi>U</mi> </msub> </semantics></math> is set to <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>100</mn> </mrow> </semantics></math>. Here, only the points of the integer numbers of antennas are valid ones (simulated ones), though we interpolate those points to make curves.</p>
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<p>Comparison of the secrecy sum rate <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>S</mi> <mi>S</mi> <mi>R</mi> </mrow> </msub> </semantics></math> of the proposed algorithms for the FDR CNOMA eavesdropping channel against the source transmit power with different <math display="inline"><semantics> <msub> <mi>α</mi> <mi>R</mi> </msub> </semantics></math> values when <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msub> <mi>N</mi> <mi>r</mi> </msub> <mo>=</mo> <msub> <mi>N</mi> <mi>t</mi> </msub> <mo>=</mo> <mn>3</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>42</mn> <mspace width="4pt"/> <mrow> <mo>(</mo> <mi>dB</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>5</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>. The path-loss from the FDR to users <math display="inline"><semantics> <msub> <mi>α</mi> <mi>U</mi> </msub> </semantics></math> is set to <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>100</mn> </mrow> </semantics></math> to scale the big <math display="inline"><semantics> <msub> <mi>P</mi> <mi>r</mi> </msub> </semantics></math> values down to realistic levels at users since the <math display="inline"><semantics> <msub> <mi>P</mi> <mi>r</mi> </msub> </semantics></math> values are taken to reflect strong SI power after the analogue SI cancellation.</p>
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<p>Comparison of the secrecy sum rate <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>S</mi> <mi>S</mi> <mi>R</mi> </mrow> </msub> </semantics></math> of the proposed algorithms for the FDR CNOMA eavesdropping channel against the FDR transmit power with different <math display="inline"><semantics> <msub> <mi>α</mi> <mi>R</mi> </msub> </semantics></math> values when <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msub> <mi>N</mi> <mi>r</mi> </msub> <mo>=</mo> <msub> <mi>N</mi> <mi>t</mi> </msub> <mo>=</mo> <mn>3</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>15</mn> <mspace width="4pt"/> <mrow> <mo>(</mo> <mi>dB</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>5</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>. The path-loss from the FDR to users <math display="inline"><semantics> <msub> <mi>α</mi> <mi>U</mi> </msub> </semantics></math> is set to <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>100</mn> </mrow> </semantics></math>.</p>
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<p>Comparison of the secrecy sum rate <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>S</mi> <mi>S</mi> <mi>R</mi> </mrow> </msub> </semantics></math> of the proposed algorithms for the FDR CNOMA eavesdropping channel against the number of FDR transmit antennas <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi>t</mi> </msub> <mo>=</mo> <msub> <mi>N</mi> <mi>r</mi> </msub> </mrow> </semantics></math> with different <math display="inline"><semantics> <msub> <mi>α</mi> <mi>R</mi> </msub> </semantics></math> values when <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>42</mn> <mspace width="4pt"/> <mrow> <mo>(</mo> <mi>dB</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>P</mi> <mi>s</mi> </msub> <mo>=</mo> <mn>15</mn> <mspace width="4pt"/> <mrow> <mo>(</mo> <mi>dB</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>/</mo> <mn>5</mn> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>R</mi> </msub> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math>. The path-loss from the FDR to users <math display="inline"><semantics> <msub> <mi>α</mi> <mi>U</mi> </msub> </semantics></math> is set to <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mn>100</mn> </mrow> </semantics></math>. Here, only the points of the integer numbers of antennas are valid ones (simulated ones), though we interpolate those points to make curves.</p>
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22 pages, 3691 KiB  
Article
G-TS-HRNN: Gaussian Takagi–Sugeno Hopfield Recurrent Neural Network
by Omar Bahou, Mohammed Roudani and Karim El Moutaouakil
Information 2025, 16(2), 141; https://doi.org/10.3390/info16020141 - 14 Feb 2025
Viewed by 288
Abstract
The Hopfield Recurrent Neural Network (HRNN) is a single-point descent metaheuristic that uses a single potential solution to explore the search space of optimization problems, whose constraints and objective function are aggregated into a typical energy function. The initial point is usually randomly [...] Read more.
The Hopfield Recurrent Neural Network (HRNN) is a single-point descent metaheuristic that uses a single potential solution to explore the search space of optimization problems, whose constraints and objective function are aggregated into a typical energy function. The initial point is usually randomly initialized, then moved by applying operators, characterizing the discrete dynamics of the HRNN, which modify its position or direction. Like all single-point metaheuristics, HRNN has certain drawbacks, such as being more likely to get stuck in local optima or miss global optima due to the use of a single point to explore the search space. Moreover, it is more sensitive to the initial point and operator, which can influence the quality and diversity of solutions. Moreover, it can have difficulty with dynamic or noisy environments, as it can lose track of the optimal region or be misled by random fluctuations. To overcome these shortcomings, this paper introduces a population-based fuzzy version of the HRNN, namely Gaussian Takagi–Sugeno Hopfield Recurrent Neural Network (G-TS-HRNN). For each neuron, the G-TS-HRNN associates an input fuzzy variable of d values, described by an appropriate Gaussian membership function that covers the universe of discourse. To build an instance of G-TS-HRNN(s) of size s, we generate s n-uplets of fuzzy values that present the premise of the Takagi–Sugeno system. The consequents are the differential equations governing the dynamics of the HRNN obtained by replacing each premise fuzzy value with the mean of different Gaussians. The steady points of all the rule premises are aggregated using the fuzzy center of gravity equation, considering the level of activity of each rule. G-TS-HRNN is used to solve the random optimization method based on the support vector model. Compared with HRNN, G-TS-HRNN performs better on well-known data sets. Full article
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<p>Illustration of the sector nonlinearity approach.</p>
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<p>Membership functions for <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p>
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<p>Gaussian Takagi–Sugeno HRNN sampling, fuzzification, and equilibrium state approximation.</p>
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<p>Illustration of the approximation of the optimal steady state via the Takagi–Sugeno HRNN sampling method.</p>
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<p>The energy of the G-TS-HRNN for different sample sizes vs. the energy of the HRNN at a steady point.</p>
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<p>Takagi–Sugeno HRNN robustness.</p>
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<p>Mean accuracy (<b>a</b>), mean F1-score (<b>b</b>), mean precision (<b>c</b>), and mean recall (<b>d</b>), on all data sets of the HRNN-SVM and the nine samples of G-TS-HRNN-SVM.</p>
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<p>Mean cpu time required by HRNN and G-TS-HRNN.</p>
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23 pages, 861 KiB  
Article
Stabilization of a Class of Fractional-Order Nonlinear Systems Subject to Actuator Saturation and Time Delay
by Esmat Sadat Alaviyan Shahri, Naser Pariz and Yangquan Chen
Appl. Sci. 2025, 15(4), 1851; https://doi.org/10.3390/app15041851 - 11 Feb 2025
Viewed by 355
Abstract
Actuator saturation and time delay are practical issues in practical control systems, significantly affecting their performance and stability. This paper addresses, for the first time, the stabilization problem of fractional-order (FO) nonlinear systems under these two practical constraints. Two primary methodologies are employed: [...] Read more.
Actuator saturation and time delay are practical issues in practical control systems, significantly affecting their performance and stability. This paper addresses, for the first time, the stabilization problem of fractional-order (FO) nonlinear systems under these two practical constraints. Two primary methodologies are employed: the vector Lyapunov function method, integrated with the M-matrix approach, and the second one is the Lyapunov-like function method, which incorporates diffusive realization and the Lipchitz condition. An optimization framework is proposed to design stabilizing controllers based on the derived stability conditions. The proposed methods are validated numerically through their application to the FO Lorenz and Liu systems, demonstrating their effectiveness in handling actuator saturation and time delay. Full article
(This article belongs to the Special Issue Dynamics and Vibrations of Nonlinear Systems with Applications)
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<p>Block diagram of the FO delayed system subject to saturation control.</p>
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<p>Phase plot of the open-loop FO Lorenz system for <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0.993</mn> </mrow> </semantics></math>.</p>
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<p>Phase plot of the closed-loop FO Lorenz system for <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0.993</mn> </mrow> </semantics></math>.</p>
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<p>The behavior of the closed-loop FO Lorenz system for <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0.993</mn> </mrow> </semantics></math>.</p>
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<p>Comparison of states of FO and integer-order system modes presented in [<a href="#B46-applsci-15-01851" class="html-bibr">46</a>].</p>
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<p>Phase plot of the open-loop FO Liu system for <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>.</p>
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<p>Phase plot of the closed-loop FO Liu system for <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>.</p>
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<p>Time evolution of state variables of the closed-loop FO Liu system for <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>.</p>
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<p>Input saturation control.</p>
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<p>Time evolution of state variables of the closed-loop FO Liu system for order <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0.78</mn> </mrow> </semantics></math>.</p>
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<p>Phase plot of the closed-loop Liu system for order <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>=</mo> <mn>0.78</mn> </mrow> </semantics></math>.</p>
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19 pages, 10147 KiB  
Article
Sparse Magnetization Vector Inversion Based on Modulus Constraints
by Yang Ou, Qingtian Lü, Jie Zhang, Yi Yang, Dingyu Jia, Yang Li, Jinghong Zhai and Zhengzhong Jiang
Remote Sens. 2025, 17(4), 597; https://doi.org/10.3390/rs17040597 - 10 Feb 2025
Viewed by 341
Abstract
Magnetization vector inversion (MVI) is an effective method for simultaneously determining the distribution of magnetization intensity and direction without knowing the direction of magnetization beforehand. Nevertheless, the presence of serious non-uniqueness in MVI imposes challenges in achieving accurate and reliable results. To improve [...] Read more.
Magnetization vector inversion (MVI) is an effective method for simultaneously determining the distribution of magnetization intensity and direction without knowing the direction of magnetization beforehand. Nevertheless, the presence of serious non-uniqueness in MVI imposes challenges in achieving accurate and reliable results. To improve the accuracy of MVI, we propose a method that incorporates a modulus constraint, informed by an analysis of the model constraints in two different frameworks. We employ a sparse operator on the magnetization magnitude and obtain an explicit expression for the magnetization components, establishing correlation constraints among them. Synthetic test results show that this method can achieve models with clear boundaries and consistent magnetization directions. Furthermore, the application of a sparse operator to the gradient’s modulus of the magnetization magnitude helps recover inclined structures. However, the dispersed magnetization directions suggest that we should also constrain the magnetization direction, simultaneously. The inversion of magnetic data measured over the Zaohuohexi iron-polymetallic deposit in Qinghai Province, northwest China, verified the proposed approach’s effectiveness. Full article
(This article belongs to the Special Issue Multi-Data Applied to Near-Surface Geophysics (Second Edition))
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<p>Magnetic anomaly data and the spatial distribution of the combined cube models: (<b>a</b>) the simulated magnetic anomaly data, mixed by Gaussian random noise with a standard deviation of 3 nT; (<b>b</b>) 3D view of the combined cube models; (<b>c</b>) horizontal slice at depth = −500 m; (<b>d</b>) vertical slice at northing = 1600 m; (<b>e</b>) vertical slice at northing = 800 m.</p>
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<p>Magnetization vector inversion result of the combined cube models’ data by employing the L<sub>2</sub> norm to the three orthogonal components: (<b>a</b>) data misfit between the predicted and observed data; (<b>b</b>) 3D view of magnetization intensity M &gt; 0.2 A/m; (<b>c</b>) horizontal slice at depth = −500 m; (<b>d</b>) vertical slice at northing = 1600 m; (<b>e</b>) vertical slice at northing = 800 m.</p>
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<p>Magnetization vector inversion result of the combined cube models’ data by employing the L<sub>0</sub> norm to the three orthogonal components: (<b>a</b>) data misfit between the predicted and observed data; (<b>b</b>) 3D view of magnetization intensity M &gt; 0.2 A/m; (<b>c</b>) horizontal slice at depth = −500 m; (<b>d</b>) vertical slice at northing = 1600 m; (<b>e</b>) vertical slice at northing = 800 m.</p>
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<p>Magnetization vector inversion result of the combined cube models’ data by employing the L<sub>0</sub> norm to the magnitude: (<b>a</b>) data misfit between the predicted and observed data; (<b>b</b>) 3D view of magnetization intensity M &gt; 0.2 A/m; (<b>c</b>) horizontal slice at depth = −500 m; (<b>d</b>) vertical slice at northing = 1600 m; (<b>e</b>) vertical slice at northing = 800 m.</p>
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<p>Statistical diagrams of the magnitude and direction of the inverted magnetization vector from the data of combined cubic models: (<b>a</b>–<b>c</b>) bar charts of the magnetization intensity; (<b>d</b>–<b>f</b>) scatter diagrams of the magnetization direction (M ≥ 0.2 A/m); (<b>a</b>,<b>d</b>) magnetization vector inversion result by employing the L<sub>2</sub> norm to the three orthogonal components; (<b>b</b>,<b>e</b>) magnetization vector inversion result by employing the L<sub>0</sub> norm to the three orthogonal components; (<b>c</b>,<b>f</b>) magnetization vector inversion result by employing the L<sub>0</sub> norm to the magnitude.</p>
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<p>Magnetic anomaly data and the spatial distribution of the combined dipping dyke models: (<b>a</b>) the simulated magnetic anomaly data, mixed by Gaussian random noise with a standard deviation of 3 nT; (<b>b</b>) 3D view of the combined dipping dyke models; (<b>c</b>) horizontal slice at depth = −400 m; (<b>d</b>) vertical slice at northing = 1200 m.</p>
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<p>Magnetization vector inversion result of the combined dipping dyke models’ data by employing the L<sub>0</sub> norm to the gradient’s components of magnetization magnitude: (<b>a</b>) data misfit between the predicted and observed data; (<b>b</b>) 3D view of magnetization intensity <span class="html-italic">M</span> &gt; 0.2 A/m; (<b>c</b>) horizontal slice at depth = −400 m; (<b>d</b>) vertical slice at northing = 1200 m.</p>
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<p>Magnetization vector inversion result of the combined dipping dyke models’ data by employing the L<sub>0</sub> norm to the gradient’s modulus of the magnetization magnitude: (<b>a</b>) data misfit between the predicted and observed data; (<b>b</b>) 3D view of magnetization intensity <span class="html-italic">M</span> &gt; 0.2 A/m; (<b>c</b>) horizontal slice at depth = −400 m; (<b>d</b>) vertical slice at northing = 1200 m.</p>
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<p>Statistical diagrams of the magnitude and direction of the inverted magnetization vector from the combined dipping dyke models’ data: (<b>a</b>,<b>b</b>) bar charts of the magnetization intensity; (<b>c</b>,<b>d</b>) scatter diagrams of the magnetization direction (M ≥ 0.2 A/m); (<b>a</b>,<b>c</b>) magnetization vector inversion by applying the L<sub>0</sub> norm to the gradient’s components of magnetization magnitude; (<b>b</b>,<b>d</b>) magnetization vector inversion by applying the L<sub>0</sub> norm to the gradient’s modulus of the magnetization magnitude.</p>
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<p>(<b>a</b>) The magnetic anomaly of the Zaohuohexi iron-polymetallic deposit, Qinghai Province, northwest China; (<b>b</b>) the residual magnetic anomaly calculated by an inversion-based method.</p>
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<p>Results of magnetization vector inversion from the Zaohuohexi magnetic data using the modulus constrains method: (<b>a</b>) 3D view of magnetization intensity <span class="html-italic">M</span> &gt; 0.3 A/m; (<b>b</b>) horizontal slice at depth = 2860 m; (<b>c</b>) vertical slice at easting = 1400 m; (<b>d</b>) vertical slice at northing = 400 m.</p>
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<p>Statistical diagrams of the inverted magnetization vector in the C1 area: (<b>a</b>) bar chart of the magnetization intensity; (<b>b</b>) scatter diagram of the magnetization direction.</p>
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14 pages, 2914 KiB  
Article
Supervised Learning Fuzzy Matrix Based on Input–Output Fuzzy Vectors
by Meili Ye, Nianliang Wang, Xianfeng Yu, Xiao Wang and Wuniu Liu
Axioms 2025, 14(2), 126; https://doi.org/10.3390/axioms14020126 - 9 Feb 2025
Viewed by 443
Abstract
Fuzzy matrices play a crucial role in fuzzy logic and fuzzy systems. This paper investigates the problem of supervised learning fuzzy matrices through sample pairs of input–output fuzzy vectors, where the fuzzy matrix inference mechanism is based on the max–min composition method. We [...] Read more.
Fuzzy matrices play a crucial role in fuzzy logic and fuzzy systems. This paper investigates the problem of supervised learning fuzzy matrices through sample pairs of input–output fuzzy vectors, where the fuzzy matrix inference mechanism is based on the max–min composition method. We propose an optimization approach based on stochastic gradient descent (SGD), which defines an objective function by using the mean squared error and incorporates constraints on the matrix elements (ensuring they take values within the interval [0, 1]). To address the non-smoothness of the max–min composition rule, a modified smoothing function for max–min is employed, ensuring stability during optimization. The experimental results demonstrate that the proposed method achieves high learning accuracy and convergence across multiple randomly generated input–output vector samples. Full article
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<p>Configuration of fuzzy matrix learning model.</p>
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<p>Max–min fuzzy function vs smoothed approximation (<math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.01</mn> <mo>,</mo> <mn>0.1</mn> </mrow> </semantics></math>).</p>
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<p>Learning progress of <math display="inline"><semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics></math> fuzzy matrix.</p>
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<p>Progressive decrease in the mean squared error.</p>
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<p>Progressive decrease in the matrix reconstruction error.</p>
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<p>Learning progress of <math display="inline"><semantics> <mrow> <mn>5</mn> <mo>×</mo> <mn>5</mn> </mrow> </semantics></math> fuzzy matrix.</p>
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<p>The MSE varies with matrix dimension <span class="html-italic">n</span> and sample size <span class="html-italic">R</span>.</p>
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<p>The reconstruction error varies with matrix dimension <span class="html-italic">n</span> and sample size <span class="html-italic">R</span>.</p>
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<p>MRE over epochs for different noise levels.</p>
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<p>MSE over epochs for different noise levels.</p>
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19 pages, 2272 KiB  
Article
Integrating Fusion Strategies and Calibration Transfer Models to Detect Total Nitrogen of Soil Using Vis-NIR Spectroscopy
by Zhengyu Tao, Anan Tao, Yi Lu, Xiaolong Li, Fei Liu and Wenwen Kong
Chemosensors 2025, 13(2), 57; https://doi.org/10.3390/chemosensors13020057 - 7 Feb 2025
Viewed by 420
Abstract
Visible near-infrared (Vis-NIR) spectroscopy is widely used for rapid soil element detection, but calibration models are often limited by instrument-specific constraints, including varying laboratory conditions and sensor configurations. To address this, we propose a novel calibration transfer method that eliminates the conventional requirement [...] Read more.
Visible near-infrared (Vis-NIR) spectroscopy is widely used for rapid soil element detection, but calibration models are often limited by instrument-specific constraints, including varying laboratory conditions and sensor configurations. To address this, we propose a novel calibration transfer method that eliminates the conventional requirement of designating ‘master’ and ‘slave’ devices. Instead, spectral data from two spectrometers are fused to create a master spectrum, while independent spectral data serve as slave spectra. We developed an ensemble stacking model, incorporating partial least squares regression (PLSR), support vector regression (SVR), and ridge regression (Ridge) in the first layer, with BoostForest (BF) as the second layer, trained on the fused master spectrum. This model was further integrated with three calibration transfer methods: direct standardization (DS), piecewise direct standardization (PDS), and spectral space transfer (SST), to enable seamless application across slave spectra. Applied to soil total nitrogen (TN) detection, the method achieved an R2P of 0.842, RMSEP of 0.017, and RPD of 2.544 on the first slave spectrometer, and an R2P of 0.830, RMSEP of 0.018, and RPD of 2.452 on the second. These results demonstrate the method’s ability to simplify calibration processes while enhancing cross-instrument prediction accuracy, supporting robust and generalizable cross-instrument applications. Full article
(This article belongs to the Special Issue Advancements of Chemical and Biosensors in China—2nd Edition)
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<p>The structure of our ensemble stacking model.</p>
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<p>Comparison flowchart depicting the standard calibration transfer method versus our novel approach. In the two spectra, the same color of the spectral lines means that they are from the same sample. The higher-resolution spectra are provided in the <a href="#app1-chemosensors-13-00057" class="html-app">Supplementary Materials</a>.</p>
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<p>The PCA chart of spectra from two spectrometers.</p>
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<p>Average spectral correlation coefficients between the master (M) spectral prediction set and the raw, DS, PDS, SST transformed slave (S) spectral prediction set.</p>
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<p>The prediction performance of the models on the (<b>a</b>) master’s calibration set, and the slave prediction sets after (<b>b</b>) DS, (<b>c</b>) PDS, and (<b>d</b>) SST transformations.</p>
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