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Keywords = optimized adaptive filling strategy

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18 pages, 5642 KiB  
Article
A New Slicer-Based Method to Generate Infill Inspired by Sandwich-Patterns for Reduced Material Consumption
by Patrick Steck, Dominik Schuler, Christian Witzgall and Sandro Wartzack
Materials 2024, 17(22), 5596; https://doi.org/10.3390/ma17225596 - 15 Nov 2024
Viewed by 352
Abstract
This work presents a novel infill method for additive manufacturing, specifically designed to optimize material use and enhance stiffness in fused filament fabrication (FFF) parts through a geometry-aware, corrugated design inspired by sandwich structures. Unlike standard infill patterns, which typically employ uniform, space-filling [...] Read more.
This work presents a novel infill method for additive manufacturing, specifically designed to optimize material use and enhance stiffness in fused filament fabrication (FFF) parts through a geometry-aware, corrugated design inspired by sandwich structures. Unlike standard infill patterns, which typically employ uniform, space-filling grids that often disregard load-specific requirements, this method generates a cavity inside the component to be printed and fill the space between inner and outer contours with continuous, adaptable extrusion paths. This design enables consistent support and improved load distribution, making it particularly effective for parts under bending stresses, as it enhances structural resilience without requiring additional material. Simulations performed on a 10 cm3 test part using this method showed potential reductions in material consumption by up to 77% and a decrease in print time by 78%, while maintaining stiffness comparable to parts using conventional 100% grid infill. Additionally, simulations demonstrated that the new corrugated infill pattern provides near-isotropic stiffness, addressing the anisotropic limitations often seen in traditional infill designs that are sensitive to load orientation. This geometry-aware infill strategy thus contributes to balanced stiffness across complex geometries, enhancing reliability under mechanical loads. By integrating directly with slicer software, this approach simplifies advanced stiffness optimization without the necessity of finite element analysis-based topology optimization. Full article
(This article belongs to the Special Issue Advanced Additive Manufacturing and Application)
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Figure 1
<p>Different adaptive infill patterns with build direction in z-axis: (<b>a</b>) Rhombic cell; (<b>b</b>) Gradual; (<b>c</b>) Cubic-subdivision.</p>
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<p>General process steps for generating G-codes. The input is an STL mesh. This mesh is then cut up. Paths are then planned from the individual slices by meshing again. The paths are then generated and finally output as G-code.</p>
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<p>Tool path generation process: This starts with the layer geometry. The wall paths are then defined. Next, an infill pattern is placed over the remaining inner geometry and, finally, the tool paths are generated.</p>
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<p>(<b>a</b>) Placement of hollowing-based infill in layers including a cavity. (<b>b</b>) Placement of corrugated infill pattern between inner and outer contours.</p>
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<p>Graphical explanation of the corrugated infill algorithm. Red dots mark the initial seed points. Blue dots mark the contact points with the outer and inner shell. Blue lines mark the contact regions (paths) with the outer and inner shell.</p>
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<p>Variation in the corrugated infill pattern by alternation of the seed path (red lines): (<b>a</b>) Unidirectional corrugated infill, in which the seeds are always placed collinear. (<b>b</b>) Bi-directional corrugated infill, in which the seeds are positioned alternately at a predefined distance. (<b>c</b>) Double-corrugated infill, in which the seeds are distributed at a constant distance from a starting point in both directions.</p>
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<p>Test part geometry: (<b>a</b>) Isometric view. (<b>b</b>) Outer dimensions of the test component for comparing the different infill types. (All units in the figure are in mm).</p>
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<p>The behavior of print time and material consumption with increasing geometry height for the different infill types using the sample geometry from <a href="#materials-17-05596-f007" class="html-fig">Figure 7</a>. The material volumes were generated simulatively using the software Klipper v0.11 (see <a href="#sec2dot2-materials-17-05596" class="html-sec">Section 2.2</a>).</p>
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<p>Geometry of the different three-point bending specimens. The geometries are simplified in the middle as symmetric.</p>
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<p>Qualitative deformation by three-point bending test using the corrugated infill as an example. The example is simplified in the middle as symmetric. The whole length of a specimen is 100 mm and the thickness is 5 mm. (Dimensions are in mm).</p>
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<p>Maximum deformation of simulative three-point bending test specimens. Gray are bending values for the infill patterns which are along the bending line, and blue are transverse to the bending line. The deformations were simulated using Ansys 2023 R2 software.</p>
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<p>Three-dimensional sketch of the test part for stiffness and stress comparison: force <math display="inline"><semantics> <msub> <mi>F</mi> <mi>z</mi> </msub> </semantics></math> and moment <math display="inline"><semantics> <msub> <mi>M</mi> <mi>y</mi> </msub> </semantics></math> are aligned in the middle of the structure, <span class="html-italic">p</span> is a pressure that occurs in the inside of the pipe. The pipe is fixed through both end surfaces in the <span class="html-italic">y</span>-direction. (All units in the figure are in mm).</p>
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<p>Analysis results (view in to x–z plane, see <a href="#materials-17-05596-f012" class="html-fig">Figure 12</a>): (<b>a</b>–<b>f</b>) Grid, (<b>g</b>–<b>l</b>) corrugated, (<b>m</b>–<b>r</b>) bi-corrugated, (<b>a</b>,<b>g</b>,<b>m</b>) bending deformation, (<b>b</b>,<b>h</b>,<b>n</b>) bending stress, (<b>c</b>,<b>i</b>,<b>o</b>) torsion deformation, (<b>d</b>,<b>j</b>,<b>p</b>) torsion stress, (<b>e</b>,<b>k</b>,<b>q</b>) pressure deformation, (<b>f</b>,<b>l</b>,<b>r</b>) pressure stress.</p>
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<p>Print time example of two different infill types. Extrusion path (black lines); travel path (red lines); start and finish point (green mark). The underlying geometry is the test geometry from <a href="#materials-17-05596-f007" class="html-fig">Figure 7</a>, scaled with a scaling factor of 10: (<b>a</b>) Conventional grid infill; (<b>b</b>) Corrugated infill.</p>
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13 pages, 4675 KiB  
Article
Hierarchical Optimal Dispatching of Electric Vehicles Based on Photovoltaic-Storage Charging Stations
by Ziyuan Liu, Junjing Tan, Wei Guo, Chong Fan, Wenhe Peng, Zhijian Fang and Jingke Gao
Mathematics 2024, 12(21), 3410; https://doi.org/10.3390/math12213410 - 31 Oct 2024
Viewed by 646
Abstract
Electric vehicles, known for their eco-friendliness and rechargeable–dischargeable capabilities, can serve as energy storage batteries to support the operation of the microgrid in certain scenarios. Therefore, photovoltaic-storage electric vehicle charging stations have emerged as an important solution to address the challenges posed by [...] Read more.
Electric vehicles, known for their eco-friendliness and rechargeable–dischargeable capabilities, can serve as energy storage batteries to support the operation of the microgrid in certain scenarios. Therefore, photovoltaic-storage electric vehicle charging stations have emerged as an important solution to address the challenges posed by energy interconnection networks. However, electric vehicle charging loads exhibit notable randomness, potentially altering load characteristics during certain periods and posing challenges to the stable operation of microgrids. To address this challenge, this paper proposes a hierarchical optimal dispatching strategy based on photovoltaic-storage charging stations. The strategy utilizes a dynamic electricity pricing model and the adaptive particle swarm optimization algorithm to effectively manage electric vehicle charging loads. By decomposing the dispatching task into multiple layers, the strategy effectively solves the problems of the “curse of dimensionality” and slow convergence associated with large numbers of electric vehicles. Simulation results demonstrate that the strategy can effectively achieve peak shaving and valley filling, reducing the load variance of the microgrid by 24.93%, and significantly reduce electric vehicle charging costs and distribution network losses, with a reduction of 92.29% in electric vehicle charging costs and 32.28% in microgrid losses compared to unorganized charging. Additionally, this strategy can meet the travel demands of electric vehicle owners while providing convenient charging services. Full article
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<p>Charging and discharging model of EV unit.</p>
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<p>Dispatching framework of PV-storage charging station.</p>
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<p>IEEE33-node system.</p>
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<p>Conventional load, PV output, and TOU electricity price of microgrid.</p>
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<p>Charging load of EV before and after scheduling.</p>
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<p>Charging and discharging power of energy storage.</p>
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<p>Load of microgrid before and after scheduling.</p>
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<p>Real-time electricity price.</p>
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<p>Voltage of distribution network nodes.</p>
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<p>Current of distribution network nodes.</p>
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<p>Network loss of distribution network.</p>
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<p>SOC of EV after scheduling.</p>
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33 pages, 8912 KiB  
Article
Real-Time Control of Thermal Synchronous Generators for Cyber-Physical Security: Addressing Oscillations with ANFIS
by Ahmed Khamees and Hüseyin Altınkaya
Processes 2024, 12(11), 2345; https://doi.org/10.3390/pr12112345 - 25 Oct 2024
Viewed by 607
Abstract
This paper introduces a novel real-time ANFIS controller, specifically designed for thermal synchronous generators, to mitigate the risks associated with cyber-physical attacks on power systems. The controller integrates the dynamic model of the turbine’s thermomechanical components, such as the boiler and heat transfer [...] Read more.
This paper introduces a novel real-time ANFIS controller, specifically designed for thermal synchronous generators, to mitigate the risks associated with cyber-physical attacks on power systems. The controller integrates the dynamic model of the turbine’s thermomechanical components, such as the boiler and heat transfer processes, within the synchronous generator. In contrast to previous studies, this model is designed for practical implementation and addresses often-overlooked areas, including the interaction between electrical and thermomechanical components, real-time control responses to cyber-physical attacks, and the incorporation of economic considerations alongside technical performance. This study takes a comprehensive approach to filling these gaps. Under normal conditions, the proposed controller significantly improves the management of industrial turbines and governors, optimizing existing control systems with a particular focus on minimizing generation costs. However, its primary innovation is its ability to respond dynamically to local and inter-area power oscillations triggered by cyber-physical attacks. In such events, the controller efficiently manages the turbines and governors of synchronous generators, ensuring the stability and reliability of power systems. This approach introduces a cutting-edge thermo-electrical control strategy that integrates both electrical and thermomechanical dynamics of thermal synchronous generators. The novelty lies in its real-time control capability to counteract the effects of cyber-physical attacks, as well as its simultaneous consideration of economic optimization and technical performance for power system stability. Unlike traditional methods, this work offers an adaptive control system using ANFIS (Adaptive NeuroFuzzy Inference System), ensuring robust performance under dynamic conditions, including interarea oscillations and voltage deviations. To validate its effectiveness, the controller undergoes extensive simulation testing in MATLAB/Simulink, with performance comparisons against previous state-of-the-art methods. Benchmarking is also conducted using IEEE standard test systems, including the IEEE 9-bus and IEEE 39-bus networks, to highlight its superiority in protecting power systems. Full article
(This article belongs to the Special Issue AI-Based Modelling and Control of Power Systems)
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<p>Conceptual model of the proposed scheme for real-time control of the generators.</p>
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<p>Proposed real-time ANFIS control flowchart for safeguarding thermal turbines from physical cyber-attacks: illustrating process stages.</p>
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<p>Schematic of gas turbine and proposed optimal ANFIS controller.</p>
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<p>Structure of neural network for proposed ANFIS controller.</p>
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<p>Input and output membership functions of the proposed ANFIS controller.</p>
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<p>Input and output membership functions of the proposed ANFIS controller.</p>
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<p>Process of choosing the best solution, feasible region, and path within the Pareto front.</p>
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<p>IEEE 9-bus case study schematic.</p>
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<p>An exploded Pareto graphic showing the best objective functions in the IEEE 9-bus network.</p>
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<p>Aggregate cost and overall speed variation of IEEE 9-bus during the event of line disconnection between nodes 5 and 7.</p>
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<p>Voltage deviation in IEEE 9-bus following line disruption between buses 5 and 7.</p>
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<p>Generators’ rotor angle and power output in IEEE 9-bus network (under permanent magnet operating condition) and during line disruption between bus 5 and bus 7.</p>
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<p>Turbine temperature of generators in IEEE 9-bus network (under permanent magnet operating condition) during line disruption between bus 5 and bus 7.</p>
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<p>Schematic of IEEE 39-bus case study.</p>
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<p>Aggregate cost and overall speed variation of IEEE 39-bus during the event of line disconnection between nodes 4 and 14. (<b>a</b>) shows the total speed deviation (in per unit) over time for different control methods: PID Control of Turbine and Governor (black), Classical Control of Turbine and Governor (red), and Optimal ANFIS Controller (blue). The optimal ANFIS controller exhibits significantly lower oscillations and faster stabilization compared to the other methods; (<b>b</b>) displays the total cost (<span>$</span>) over time for the same control methods. The Optimal ANFIS Controller consistently results in the lowest operational cost, followed by the Classical Control and PID Control methods.</p>
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<p>Voltage deviation in IEEE 39-bus following line disruption between buses 4 and 14.</p>
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<p>Mechanical output power in IEEE 39-bus network (under permanent magnet operating condition) and during line disruption between bus 4 and bus 14.</p>
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<p>Turbine temperature of generators in IEEE 39-bus network (under permanent magnet operating condition) and during line disruption between bus 4 and bus 14.</p>
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13 pages, 3302 KiB  
Article
ADPA Optimization for Real-Time Energy Management Using Deep Learning
by Zhengdong Wan, Yan Huang, Liangzheng Wu and Chengwei Liu
Energies 2024, 17(19), 4821; https://doi.org/10.3390/en17194821 - 26 Sep 2024
Viewed by 519
Abstract
The current generation of renewable energy remains insufficient to meet the demands of users within the network, leading to the necessity of curtailing flexible loads and underscoring the urgent need for optimized microgrid energy management. In this study, the deep learning-based Adaptive Dynamic [...] Read more.
The current generation of renewable energy remains insufficient to meet the demands of users within the network, leading to the necessity of curtailing flexible loads and underscoring the urgent need for optimized microgrid energy management. In this study, the deep learning-based Adaptive Dynamic Programming Algorithm (ADPA) was introduced to integrate real-time pricing into the optimization of demand-side energy management for microgrids. This approach not only achieved a dynamic balance between supply and demand, along with peak shaving and valley filling, but it also enhanced the rationality of energy management strategies, thereby ensuring stable microgrid operation. Simulations of the Real-Time Electricity Price (REP) management model under demand-side response conditions validated the effectiveness and feasibility of this approach in microgrid energy management. Based on the deep neural network model, optimization of the objective function was achieved with merely 54 epochs, suggesting a highly efficient computational process. Furthermore, the integration of microgrid energy management with the REP conformed to the distributed multi-source power supply microgrid energy management and scheduling and improved the efficiency of clean energy utilization significantly, supporting the implementation of national policies aimed at the development of a sustainable power grid. Full article
(This article belongs to the Section F5: Artificial Intelligence and Smart Energy)
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<p>Deep learning ADPA: (<b>a</b>) fundamental framework; (<b>b</b>) multilayer neural network topology.</p>
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<p>Power generation: (<b>a</b>) hydroelectric power generation; (<b>b</b>) gas power generation; (<b>c</b>) distributed power storage device.</p>
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<p>Objective function setting and output training process: (<b>a</b>) error optimization process; (<b>b</b>) iterative regression process; and (<b>c</b>) the number of iterations of the best-fit parameter under the minimum error.</p>
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<p>REP of microgrid and corresponding purchased electricity: (<b>a</b>) REP corresponding to the purchase of electricity; (<b>b</b>) REP corresponding to supply–demand balance.</p>
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<p>Relationships between REP and microgrid power supply and demand: (<b>a</b>) the relationship between the total supply and total demand; (<b>b</b>) the relationship between the power and rigid-load and maximum power demands.</p>
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25 pages, 12356 KiB  
Article
Efficient On-Board Compression for Arbitrary-Shaped Cloud-Covered Remote Sensing Images via Adaptive Filling and Controllable Quantization
by Keyan Wang, Jia Jia, Peicheng Zhou, Haoyi Ma, Liyun Yang, Kai Liu and Yunsong Li
Remote Sens. 2024, 16(18), 3431; https://doi.org/10.3390/rs16183431 - 15 Sep 2024
Viewed by 678
Abstract
Due to the fact that invalid cloud-covered regions in remote sensing images consume a considerable quantity of coding bit rates under the limited satellite-to-ground transmission rate, existing image compression methods suffer from low compression efficiency and poor reconstruction quality, especially in cloud-free regions [...] Read more.
Due to the fact that invalid cloud-covered regions in remote sensing images consume a considerable quantity of coding bit rates under the limited satellite-to-ground transmission rate, existing image compression methods suffer from low compression efficiency and poor reconstruction quality, especially in cloud-free regions which are generally regarded as regions of interest (ROIs). Therefore, we propose an efficient on-board compression method for remote sensing images with arbitrary-shaped clouds by leveraging the characteristics of cloudy images. Firstly, we introduce two novel spatial preprocessing strategies, namely, the optimized adaptive filling (OAF) strategy and the controllable quantization (CQ) strategy. Specifically, the OAF strategy fills each cloudy region using the contextual information at its inner and outer edge to completely remove the information of cloudy regions and minimize their coding consumption, which is suitable for images with only thick clouds. The CQ strategy implicitly identifies thin and thick clouds and rationally quantifies the data in cloudy regions to alleviate information loss in thin cloud-covered regions, which can achieve the balance between coding efficiency and reconstructed image quality and is more suitable for images containing thin clouds. Secondly, we develop an efficient coding method for a binary cloud mask to effectively save the bit rate of the side information. Our method provides the flexibility for users to choose the desired preprocessing strategy as needed and can be embedded into existing compression framework such as JPEG2000. Experimental results on the GF-1 dataset show that our method effectively reduces the coding consumption of invalid cloud-covered regions and significantly improve the compression efficiency as well as the quality of decoded images. Full article
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<p>The categories of clouds in the remote sensing image. (<b>a</b>,<b>b</b>) are thick clouds, (<b>c</b>) is thin cloud. The close-up views of the regions marked by red boxes are shown at the bottom right corner.</p>
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<p>Intensity histograms of cloud-free remote sensing images. (<b>a</b>–<b>c</b>) are the original images. (<b>d</b>–<b>f</b>) are the corresponding gray value histograms of (<b>a</b>–<b>c</b>), respectively.</p>
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<p>Intensity histograms of cloud-covered remote sensing images. (<b>a</b>,<b>f</b>,<b>k</b>) are the original images. (<b>b</b>,<b>g</b>,<b>l</b>) are cloud masks of (<b>a</b>), (<b>f</b>), (<b>k</b>), respectively. (<b>c</b>,<b>h</b>,<b>m</b>) are histograms of (<b>a</b>), (<b>f</b>), (<b>k</b>), respectively. (<b>d</b>,<b>i</b>,<b>n</b>) are histograms of ground object of (<b>a</b>), (<b>f</b>), (<b>k</b>), respectively. (<b>e</b>,<b>j</b>,<b>o</b>) are histograms of cloudy regions of (<b>a</b>), (<b>f</b>), (<b>k</b>), respectively.</p>
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<p>The overall codec framework.</p>
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<p>The processing flow of the optimized adaptive filling strategy.</p>
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<p>Schematic diagram of boundary filtering on the filled cloudy region.</p>
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<p>Comparison of cloudy region filling by using the preprocessing modules of different image compression methods. (<b>a</b>) is original image. (<b>b</b>) is cloud mask of (<b>a</b>), where white regions (gray value of 255) denote clouds and black regions (gray value of 0) denote ground objects. (<b>c</b>–<b>e</b>) are results of filling the cloudy region using ADR, LEC, and OAF (our method), respectively. The close-up views of the regions marked by red boxes are shown at the bottom right corner, which clearly shows the smoothness of the boundary after filling cloudy regions with different strategies.</p>
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<p>Results of different quantization methods. (<b>a</b>) is original image. (<b>b</b>) is cloud mask of (<b>a</b>). (<b>c</b>) is the result of quantization. (<b>d</b>) is the result of CQ. The close-up views of the regions marked by red boxes are shown at the bottom right corner.</p>
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<p>The processing flow of the controllable quantization strategy. The close-up views of the regions marked by red boxes are shown at the bottom right corner.</p>
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<p>The quantization of the data in cloudy regions in the spatial domain. The close-up views of the regions marked by red boxes in the original image are shown at the bottom left corner.</p>
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<p>The processing flow of binary cloud mask encoding.</p>
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<p>The processing flow of symbol packaging.</p>
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<p>The contrast of the decoded images before and after image post-processing. (<b>a</b>) is original image, (<b>b</b>) is cloud mask of (<b>a</b>). (<b>c</b>) OAF without post-processing, (<b>d</b>) OAF with post-processing, (<b>e</b>) CQ without post-processing, (<b>f</b>) CQ with post-processing.</p>
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<p>Examples of evaluation dataset. (<b>a</b>–<b>e</b>) are GF-1 remote sensing images including ice and snow, water, urban area, farmland, and forest, respectively, (<b>f</b>), (<b>g</b>), (<b>h</b>), (<b>i</b>), (<b>j</b>) are the corresponding cloud masks of (<b>a</b>), (<b>b</b>), (<b>c</b>), (<b>d</b>), (<b>e</b>) respectively.</p>
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<p>The decoded images by using CQ with different S and D values. The close-up views of the regions marked by red boxes are shown at the top right corner and the top left corner. (<b>a</b>) is original image, (<b>b</b>) is cloud mask of (<b>a</b>). (<b>c</b>) D = 0, S = 0, <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 60.14 dB, (<b>d</b>) D = 0, S = 2, <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 62.83 dB, (<b>e</b>) D = 0, S = 4, <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 63.54 dB, (<b>f</b>) D = 0, S = 6, <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 65.21 dB, (<b>g</b>) D = 4, S = 2, <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 63.01 dB, (<b>h</b>) D = 4, S = 4, <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 63.87 dB, (<b>i</b>) D = 16, S = 2, <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 63.95 dB.</p>
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<p>Image 1.The percentage of clouds was 50%. (<b>a</b>) is original image, (<b>b</b>) is cloud mask of (<b>a</b>). The close-up views of the regions marked by red boxes are shown at the top left corner and the bottom left corner.</p>
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<p>Image 2. The percentage of could was 50%. (<b>a</b>) is original image, (<b>b</b>) is cloud mask of (<b>a</b>). The close-up views of the regions marked by red boxes are shown at the bottom left corner.</p>
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<p>Comparison of subjective quality of decoded image 1. The close-up views of the regions marked by red boxes are shown at the bottom left corner and the top left corner. The compression ratio was 4. (<b>a</b>) JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 61.98 dB, (<b>b</b>) ADR + JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 65.61 dB, (<b>c</b>) LEC + JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 66.48 dB, (<b>d</b>) OAF + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 67.75 dB, (<b>e</b>) CQ (D = 4, S = 2) + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 64.70 dB, (<b>f</b>) CQ (D = 1024, S = 10) + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 67.18 dB.</p>
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<p>Comparison of subjective quality of the decoded image of image 1. The close-up views of the regions marked by red boxes are shown at the bottom left corner and the top left corner. The compression ratio was 64. (<b>a</b>) JPEG2000. <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 32.76 dB, (<b>b</b>) ADR + JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 32.98 dB, (<b>c</b>) LEC + JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 33.50 dB, (<b>d</b>) OAF + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math><math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 34.97 dB, (<b>e</b>) CQ (D = 4, S = 2) + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 33.45 dB, (<b>f</b>) CQ (D = 1024, S = 10) + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 34.04 dB.</p>
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<p>Comparison of subjective quality of the decoded image of image 2. The close-up views of the regions marked by red boxes are shown at the bottom left corner and the top left corner. The compression ratio was 4. (<b>a</b>) JPEG2000. <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 61.84 dB, (<b>b</b>) ADR + JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 64.55 dB, (<b>c</b>) LEC + JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 66.71 dB, (<b>d</b>) OAF + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 69.69 dB, (<b>e</b>) CQ (D = 4, S = 2) + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 65.22 dB, (<b>f</b>) CQ (D = 1024, S = 10) + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 69.01 dB.</p>
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<p>Comparison of subjective quality of the decoded image of image 2. The close-up views of the regions marked by red boxes are shown at the bottom left corner. The compression ratio was 64. (<b>a</b>) JPEG2000. <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 28.45dB, (<b>b</b>) ADR + JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 32.38 dB, (<b>c</b>) LEC + JPEG2000 <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 33.73 dB, (<b>d</b>) OAF + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 36.53 dB, (<b>e</b>) CQ (D = 4, S = 2) + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 33.82 dB, (<b>f</b>) CQ (D = 1024, S = 10) + JPEG2000(<math display="inline"><semantics> <mrow> <mi>D</mi> <msub> <mi>C</mi> <mrow> <mi>o</mi> <mi>p</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>) <math display="inline"><semantics> <mrow> <mi>P</mi> <mi>S</mi> <mi>N</mi> <msub> <mi>R</mi> <mrow> <mi>R</mi> <mi>O</mi> <mi>I</mi> </mrow> </msub> </mrow> </semantics></math> = 36.13 dB.</p>
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26 pages, 10477 KiB  
Article
Interval Constrained Multi-Objective Optimization Scheduling Method for Island-Integrated Energy Systems Based on Meta-Learning and Enhanced Proximal Policy Optimization
by Dongbao Jia, Ming Cao, Jing Sun, Feimeng Wang, Wei Xu and Yichen Wang
Electronics 2024, 13(17), 3579; https://doi.org/10.3390/electronics13173579 - 9 Sep 2024
Cited by 1 | Viewed by 664
Abstract
Multiple uncertainties from source–load and energy conversion significantly impact the real-time dispatch of an island integrated energy system (IIES). This paper addresses the day-ahead scheduling problems of IIES under these conditions, aiming to minimize daily economic costs and maximize the output of renewable [...] Read more.
Multiple uncertainties from source–load and energy conversion significantly impact the real-time dispatch of an island integrated energy system (IIES). This paper addresses the day-ahead scheduling problems of IIES under these conditions, aiming to minimize daily economic costs and maximize the output of renewable energies. We introduce an innovative algorithm for Interval Constrained Multi-objective Optimization Problems (ICMOPs), which incorporates meta-learning and an improved Proximal Policy Optimization with Clipped Objective (PPO-CLIP) approach. This algorithm fills a notable gap in the application of DRL to complex ICMOPs within the field. Initially, the multi-objective problem is decomposed into several single-objective problems using a uniform weight decomposition method. A meta-model trained via meta-learning enables fine-tuning to adapt solutions for subsidiary problems once the initial training is complete. Additionally, we enhance the PPO-CLIP framework with a novel strategy that integrates probability shifts and Generalized Advantage Estimation (GAE). In the final stage of scheduling plan selection, a technique for identifying interval turning points is employed to choose the optimal plan from the Pareto solution set. The results demonstrate that the method not only secures excellent scheduling solutions in complex environments through its robust generalization capabilities but also shows significant improvements over interval-constrained multi-objective evolutionary algorithms, such as IP-MOEA, ICMOABC, and IMOMA-II, across multiple multi-objective evaluation metrics including hypervolume (HV), runtime, and uncertainty. Full article
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<p>IIES architecture.</p>
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<p>MOMAML-PPO solution process.</p>
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<p>Solution selection at interval knee points.</p>
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<p>Meta-learning training.</p>
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<p>Schematic of the enhanced PPO-CLIP method.</p>
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<p>Forecasting renewable energy output and multiple load demands.</p>
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<p>Comparison of wind power output intervals under different confidence levels.</p>
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<p>The 95% confidence interval forecasting for renewable energy output and load demands.</p>
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<p>Pareto frontier of the ICMOP solution. (<b>a</b>) Pareto front boundary point plot; (<b>b</b>) Pareto front matrix plot.</p>
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<p>Scheduling results.</p>
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<p>Sensitivity analysis of the learning rate parameter in actor–critic networks.</p>
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<p>Sensitivity analysis of the reward discount factor in coefficient parameters.</p>
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<p>Average reward change curve.</p>
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<p>Dispatch strategy under emergency conditions: (<b>a</b>) scheduling results for Emergent Scenario 1; (<b>b</b>) scheduling results for Emergent Scenario 2.</p>
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21 pages, 9112 KiB  
Article
Stepwise Construction and Integration of Ecological Network in Resource-Based Regions: A Case Study on Liaoning Province, China
by Shaoqing Wang, Yanling Zhao, He Ren and Shichao Zhu
Remote Sens. 2024, 16(17), 3228; https://doi.org/10.3390/rs16173228 - 31 Aug 2024
Viewed by 550
Abstract
Ecological networks are an effective strategy to maintain regional ecological security. However, current research on ecological network construction in areas with large-scale resource extraction is limited. Moreover, classic ecological network construction methods do not perform satisfactorily when implemented in heavily damaged mining landscapes. [...] Read more.
Ecological networks are an effective strategy to maintain regional ecological security. However, current research on ecological network construction in areas with large-scale resource extraction is limited. Moreover, classic ecological network construction methods do not perform satisfactorily when implemented in heavily damaged mining landscapes. Taking the example of Liaoning Province, China, a framework for stepwise renewal of ecological networks was proposed, which integrates basic ecological sources and other sources that include mining areas. The framework was based on multi-source ecological environment monitoring data, and all potential ecological sources were extracted and screened using an MSPA model and the area threshold method. Further, ecological sources were classified into two types and three levels based on the influence of abandoned mines and the characteristics of ecosystem services in the ecological sources. Ecological corridors were extracted using the MCR model. An ecological corridor optimization process based on combining the gravity model with addition and removal rules of corridors was proposed. The results indicated that the basic ecological network in Liaoning Province included 101 ecological sources and 162 ecological corridors, and the supplementary ecological network included 28 ecological sources and 67 ecological corridors. The ecological sources were divided into two types, and corridors were divided into three types. The basic ecological network exhibited a spatial distribution of discrete connections in the west and close connections in the east. Changes in ecological network topological indicators indicated that a supplementary ecological network strengthened the structural performance of the regional ecological network, expanding spatial coverage, filling hollow areas, and enriching local details of the regional ecological network. Regulation strategies were proposed for ecological sources with different connection modes. The number of ecological sources implementing restrictive development, pattern optimization, and protective development were 101, 12, and 16, respectively. This paper provides a constructing framework of ecological networks adapted for resource-based regions. This method can support decisions for the environmental governance of mines, thus contributing to a balance between resource exploitation and ecological protection in regions. Full article
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<p>Geographical location and land cover in Liaoning Province.</p>
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<p>Methodological framework used to construct and integrate ecological network.</p>
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<p>Stepwise integration model of ecological network of basic ecological network and supplementary ecological network.</p>
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<p>Distribution and classification of ecological sources.</p>
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<p>Resistance surface of every factor and modified comprehensive resistance surface. (<b>a</b>) represents the resistance surface of DEM; (<b>b</b>) represents the ecological risk index based on the land cover; (<b>c</b>) represents the resistance surface of land cover; (<b>d</b>) represents the resistance surface of vegetation coverage; (<b>e</b>) represents the resistance surface of the slope; and (<b>f</b>) represents the modified resistance surface.</p>
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<p>Spatial patterns of optimization of a basic ecological network.</p>
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<p>Spatial patterns of integration of two types of ecological network. (<b>a</b>) represents the integration of the basic ecological network and level 1 supplementary ecological network; (<b>b</b>) represents the integration of the basic ecological network and level 2 supplementary ecological network; (<b>c</b>) represents the integration of the basic ecological network and level 2 supplementary ecological network.</p>
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<p>Spatial patterns of integration of all ecological networks.</p>
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<p>Regulation strategies with ecological sources.</p>
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19 pages, 13916 KiB  
Article
Hole Appearance Constraint Method in 2D Structural Topology Optimization
by Lei Zhu, Tongxing Zuo, Chong Wang, Qianglong Wang, Zhengdong Yu and Zhenyu Liu
Mathematics 2024, 12(17), 2645; https://doi.org/10.3390/math12172645 - 26 Aug 2024
Viewed by 590
Abstract
A 2D topology optimization algorithm is proposed, which integrates the control of hole shape, hole number, and the minimum scale between holes through the utilization of an appearance target image. The distance between the structure and the appearance target image is defined as [...] Read more.
A 2D topology optimization algorithm is proposed, which integrates the control of hole shape, hole number, and the minimum scale between holes through the utilization of an appearance target image. The distance between the structure and the appearance target image is defined as the hole appearance constraint. The appearance constraint is organized as inequality constraints to control the performance of the structure in an iterative optimization. Specifically, hole shapes are controlled by matching adaptable equivalent shape templates, the minimum scales between holes are controlled by a hole shrinkage strategy, and the hole number is controlled by a hole number calculation and filling method. Based on the SIMP interpolation topology optimization model, the effectiveness of the proposed method is verified through numerical examples. Full article
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<p>Optimization algorithm flowchart for hole appearance constraints.</p>
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<p>Image processing and hole information extraction. (<b>a</b>) Grayscale Image. (<b>b</b>) Binary Image. (<b>c</b>) Hole Information Image. (<b>d</b>) Enclosed Solid Regions. (<b>e</b>) Boundary Image of Solid Regions.</p>
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<p>Effectiveness of the MBR algorithm for holes. The red box represents the MBR of each hole.</p>
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<p>Example of similarity measurement methods for three equivalent shapes of holes. (<b>a</b>) Hole shape. (<b>b</b>) Rectangularity measurement method. (<b>c</b>) Ellipticity measurement method. (<b>d</b>) Isosceles triangle measurement method.</p>
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<p>Relationship between shape parameters of equivalent shapes and aspect ratio. The red box represents the the MBR of equivalent shape. (<b>a</b>) The relationship between the parameters of a rectangle and its aspect ratio. (<b>b</b>) The Relationship between Elliptical Parameters and Aspect Ratio. (<b>c</b>,<b>d</b>) The two relationships between the parameters and aspect ratio of isosceles triangles.</p>
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<p>Method for determining the angle <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>θ</mi> </mrow> <mo stretchy="false">^</mo> </mover> </mrow> </semantics></math> of the equivalent shape. The red box represents the equivalent rectangle of the shape.</p>
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<p>Example of hole shapes and their <math display="inline"><semantics> <mrow> <mi>T</mi> <mi>r</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>e</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>E</mi> <mi>l</mi> </mrow> </semantics></math> values. The red box represents the equivalent shape.</p>
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<p>Hole filling method. (<b>a</b>) Binary image of structure. (<b>b</b>) The appearance target image obtained by filling an extra hole.</p>
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<p>Generating appearance targets through mapping equivalent shapes to a fixed grid. (<b>a</b>) The MES of each hole. The red box represents the equivalent shape of each hole. (<b>b</b>) Solid region after hole filling. (<b>c</b>) Visual representation of the target image. The red box represents the equivalent shape of the hole corresponding to the structure in (<b>a</b>).</p>
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<p>Schematic diagram of mitigating hole interference and minimum distance between cavities using hole shrinking strategy. (<b>a</b>) The grayscale image. (<b>b</b>) Binary image of structure. (<b>c</b>) The MES of each hole. The red box represents the equivalent shape of each hole. (<b>d</b>) The appearance target image. (<b>e</b>) Expand the holes in the appearance target image. (<b>f</b>) Updated appearance target image by hole shrinking strategy.</p>
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<p>Design domain and optimization results. (<b>a</b>) Design domain. (<b>b</b>) The structure obtained in the first phase of our optimization algorithm.</p>
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<p>Results of hole regularization for different values of <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>A</mi> </mrow> <mrow> <mi mathvariant="normal">*</mi> </mrow> </msup> </mrow> </semantics></math>.</p>
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<p>The change in compliance, volume fraction, and appearance constraint during the iteration process. (<b>a</b>) The change in compliance changes during the iteration process. (<b>b</b>) The change in volume fraction and appearance constraint during the iteration process. The blue line represents the volume fraction, and the orange line represents the appearance constraint.</p>
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<p>Optimization results using single shape templates. (<b>a</b>) Isosceles triangle template. (<b>b</b>) Rectangle template. (<b>c</b>) Ellipse template.</p>
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<p>Design domain and optimization results. (<b>a</b>) Design domain. (<b>b</b>) Structure gray image.</p>
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<p>Effects of different minimum distance constraints between holes. The structure within the large red circle represents the enlarged structure within the small red circle.</p>
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<p>The change in compliance, volume fraction, and appearance constraints during the iteration process. (<b>a</b>) The change in compliance during the iteration process when k takes different values. (<b>b</b>) The change in volume fraction during the iteration process when k takes different values. (<b>c</b>) The change in appearance constraints during the iteration process when k takes different values.</p>
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<p>The effect of hole regularization under different hole quantity constraints.</p>
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<p>Volume fraction and appearance constraint during the iteration process for <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>m</mi> </mrow> <mo>¯</mo> </mover> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>. At the 33rd iteration, the number of holes reaches 4, and the optimization process transitions into the second stage, where appearance constraint is applied. The blue line represents the volume fraction, and the orange line represents the appearance con-straint.</p>
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<p>The optimization outcomes for the MBB beam case study.</p>
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23 pages, 1362 KiB  
Article
Joint Optimization of Service Migration and Resource Allocation in Mobile Edge–Cloud Computing
by Zhenli He, Liheng Li, Ziqi Lin, Yunyun Dong, Jianglong Qin and Keqin Li
Algorithms 2024, 17(8), 370; https://doi.org/10.3390/a17080370 - 21 Aug 2024
Viewed by 899
Abstract
In the rapidly evolving domain of mobile edge–cloud computing (MECC), the proliferation of Internet of Things (IoT) devices and mobile applications poses significant challenges, particularly in dynamically managing computational demands and user mobility. Current research has partially addressed aspects of service migration and [...] Read more.
In the rapidly evolving domain of mobile edge–cloud computing (MECC), the proliferation of Internet of Things (IoT) devices and mobile applications poses significant challenges, particularly in dynamically managing computational demands and user mobility. Current research has partially addressed aspects of service migration and resource allocation, yet it often falls short in thoroughly examining the nuanced interdependencies between migration strategies and resource allocation, the consequential impacts of migration delays, and the intricacies of handling incomplete tasks during migration. This study advances the discourse by introducing a sophisticated framework optimized through a deep reinforcement learning (DRL) strategy, underpinned by a Markov decision process (MDP) that dynamically adapts service migration and resource allocation strategies. This refined approach facilitates continuous system monitoring, adept decision making, and iterative policy refinement, significantly enhancing operational efficiency and reducing response times in MECC environments. By meticulously addressing these previously overlooked complexities, our research not only fills critical gaps in the literature but also enhances the practical deployment of edge computing technologies, contributing profoundly to both theoretical insights and practical implementations in contemporary digital ecosystems. Full article
(This article belongs to the Collection Feature Papers in Algorithms for Multidisciplinary Applications)
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<p>An example of an MECC environment.</p>
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<p>An example of the migration process.</p>
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<p>Training of A2C-based dynamic migration and resource allocation algorithm.</p>
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<p>The impact of the number of ESs on average response delay.</p>
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<p>The impact of the number of ESs on failure rate.</p>
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<p>The impact of the time constraint on average response delay.</p>
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<p>The impact of the time constraint on failure rate.</p>
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<p>The impact of the number of users on average response delay.</p>
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<p>Decision-making duration for each step.</p>
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<p>The impact of the number of users on failure rate.</p>
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<p>The impact of data size on average response delay.</p>
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<p>The impact of data size on average failure rate.</p>
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<p>The impact of network scale expansion in an environment with 40 users and 20 ESs. (<b>a</b>) Average response delay. (<b>b</b>) Average failure rate.</p>
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21 pages, 34151 KiB  
Article
Analyzing Spatial Dependence of Rice Production in Northeast Thailand for Sustainable Agriculture: An Optimal Copula Function Approach
by Suneerat Srisopa, Peerapong Luamka, Saowanee Rattanawan, Khanitta Somtrakoon and Piyapatr Busababodhin
Sustainability 2023, 15(20), 14774; https://doi.org/10.3390/su152014774 - 11 Oct 2023
Viewed by 1956
Abstract
Rice is not only central to Thailand’s economy and dietary consumption but also plays a significant role in global food security. Northeast Thailand, in particular, is a principal region for rice cultivation. However, with the mounting concerns of climate change, it becomes paramount [...] Read more.
Rice is not only central to Thailand’s economy and dietary consumption but also plays a significant role in global food security. Northeast Thailand, in particular, is a principal region for rice cultivation. However, with the mounting concerns of climate change, it becomes paramount to understand the interplay between regional weather patterns and rice yields, aiming to develop effective adaptive agricultural strategies. The current study aimed to fill the research gap by investigating an optimal copula for the spatial dependence of rice production and related meteorological variables in this area. The objective of this study is to understand how rice production in different areas relates to each other in order to improve farming practices and address challenges such as suitable weather. To achieve this goal, we apply three families of copulas—elliptical, Archimedean, and extreme—to analyze crop and meteorological variables across the watershed in the northeastern region of Thailand. With a data foundation extending from 1981 to 2021 from the Regional Office of Agricultural Economics Sector 4, Thailand, this study offers a comprehensive analysis of the spatial dynamics driving rice production across twenty provinces in Northeast Thailand. Using a piecewise linear model, we dissected rice yield trends, revealing distinct slopes in production and yield across various periods. The analysis leaned on elliptical, Archimedean, and extreme copula families, using the maximum likelihood estimation to discern marginal distribution residuals. Through rigorous bootstrap goodness-of-fit tests and cross-validation, the most appropriate copula for each province was identified. Key findings demonstrate pronounced spatial interdependencies in rice yields, with the Frank copula prominently capturing the product relationship between provinces such as Maha Sarakham and Roi-Et. Conversely, the Clayton copula better characterized regions such as Srisaket and Ubon Ratchathani. Moreover, the results underscore the considerable influence of meteorological factors, notably rainfall and temperature, on rice production, especially in regions like Ubon Ratchathani. In distilling these multifaceted relationships, the study charts a pathway for crafting sustainable, localized agricultural strategies. As the world grapples with climate change’s ramifications, the insights from this research stand crucial, offering direction for fostering resilience, adaptation, and optimizing rice productivity across Thailand’s diverse agrarian landscapes. Full article
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<p>Land use map of the northeastern region of Thailand.</p>
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<p>Box-plot illustrating key meteorological metrics for the Northeast (1981–2021): (<b>a</b>) mean rainfall (mm), (<b>b</b>) mean temperature (°C), (<b>c</b>) total rainfall accumulation (mm), and (<b>d</b>) mean relative humidity (%).</p>
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<p>Changes in rice yield from 1981 to 2021 in two combinations of productivity and area for wet seasons with segmented regression lines at Ubon Ratchathani province. Symbols * and *** denote significance levels of 0.05 and 0.001, respectively.</p>
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<p>Comparison of rice production and yield for Ubon Ratchathani Province. (<b>a</b>) Rice production and cultivation areas from 1991 to 2021. (<b>b</b>) Evolution of rice production and yield over the period 1981 to 2021. Symbols *, **, and *** denote significance levels of 0.05, 0.01, and 0.001, respectively.</p>
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<p>Comparison of rice production and yield for Ubon Ratchathani Province. (<b>a</b>) Rice production and cultivation areas from 1991 to 2021. (<b>b</b>) Evolution of rice production and yield over the period 1981 to 2021. Symbols *, **, and *** denote significance levels of 0.05, 0.01, and 0.001, respectively.</p>
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<p>Comparison of rice production and yield for Udonthani Province. (<b>a</b>) Rice production and cultivation areas from 1991 to 2021. (<b>b</b>) Evolution of rice production and yield over the period 1981 to 2021. Symbols * and *** denote significance levels of 0.05 and 0.001, respectively.</p>
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<p>Comparison of rice production and yield for Udonthani Province. (<b>a</b>) Rice production and cultivation areas from 1991 to 2021. (<b>b</b>) Evolution of rice production and yield over the period 1981 to 2021. Symbols * and *** denote significance levels of 0.05 and 0.001, respectively.</p>
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<p>Comparison of rice production and yield for Roi-Et province. (<b>a</b>) Rice production and cultivation areas from 1991 to 2021. (<b>b</b>) Evolution of rice production and yield over the period 1981 to 2021. Symbols ** and *** denote significance levels of 0.01 and 0.001, respectively.</p>
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<p>Comparison of rice production and yield for Roi-Et province. (<b>a</b>) Rice production and cultivation areas from 1991 to 2021. (<b>b</b>) Evolution of rice production and yield over the period 1981 to 2021. Symbols ** and *** denote significance levels of 0.01 and 0.001, respectively.</p>
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<p>Comparison of rice production and yield for Burirum province. (<b>a</b>) Rice production and cultivation areas from 1991 to 2021. (<b>b</b>) Evolution of rice production and yield over the period 1981 to 2021. Symbols * and *** denote significance levels of 0.05 and 0.001, respectively.</p>
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<p>Comparison of rice production and yield for Burirum province. (<b>a</b>) Rice production and cultivation areas from 1991 to 2021. (<b>b</b>) Evolution of rice production and yield over the period 1981 to 2021. Symbols * and *** denote significance levels of 0.05 and 0.001, respectively.</p>
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<p>Relationship of yields (kg/ha) across regions.</p>
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<p>Association between crop data and meteorological variables in Ubon Rachathani province.</p>
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<p>Comparison of empirical copulas and fitted copula between Maha Sarakham and Roi-Et province.</p>
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<p>Comparison of empirical copulas and fitted copula between yields and meteorological data at Ubon Ratchathani province. (<b>a</b>) Yield and average rainfall (mm), (<b>b</b>) Yield and average temperature (°), (<b>c</b>) Yield and cumulative rainfall (mm) and (<b>d</b>) Yield and relative humidity (%).</p>
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17 pages, 1172 KiB  
Article
V2G Scheduling of Electric Vehicles Considering Wind Power Consumption
by Bingjie Shang, Nina Dai, Li Cai, Chenxi Yang, Junting Li and Qingshan Xu
World Electr. Veh. J. 2023, 14(9), 236; https://doi.org/10.3390/wevj14090236 - 28 Aug 2023
Cited by 6 | Viewed by 1555
Abstract
The wind power (WP) has strong random volatility and is not coordinated with the load in time and space, resulting in serious wind abandonment. Based on this, an orderly charging and discharging strategy for electric vehicles (EVs) considering WP consumption is proposed in [...] Read more.
The wind power (WP) has strong random volatility and is not coordinated with the load in time and space, resulting in serious wind abandonment. Based on this, an orderly charging and discharging strategy for electric vehicles (EVs) considering WP consumption is proposed in this paper. The strategy uses the vehicle-to-grid (V2G) technology to establish the maximum consumption of WP in the region, minimizes the peak–valley difference of the power grid and maximizes the electricity sales efficiency of the power company in the mountainous city. The dynamic electricity prices are set according to the predicted values and the true values of WP output, and the improved adaptive particle swarm optimization (APSO) and CVX toolbox are used to solve the problems. When the user responsiveness is 30%, 60% and 100%, the WP consumption is 72.1%, 81.04% and 92.69%, respectively. Meanwhile, the peak shaving and valley filling of the power grid are realized, and the power sales benefit of the power company is guaranteed. Full article
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<p>The daily mileage of EVs.</p>
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<p>Daily required charging capacity of EV.</p>
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<p>Charging start time and distribution.</p>
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<p>Charging and discharging flow chart.</p>
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<p>The WP decomposed by VMD.</p>
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<p>One-day WP prediction and error analysis in summer.</p>
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<p>Electricity price distribution.</p>
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<p>PSO solution flow chart.</p>
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<p>Load superposition diagram.</p>
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<p>Comparison of basic load, disorderly charging and orderly charging load.</p>
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<p>WP consumption under basic load, disorderly and orderly charging.</p>
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<p>V2G optimization under different responsiveness.</p>
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<p>WP accommodation under different responsiveness.</p>
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24 pages, 14256 KiB  
Article
A Novel Framework for Stratified-Coupled BLS Tree Trunk Detection and DBH Estimation in Forests (BSTDF) Using Deep Learning and Optimization Adaptive Algorithm
by Huacong Zhang, Huaiqing Zhang, Keqin Xu, Yueqiao Li, Linlong Wang, Ren Liu, Hanqing Qiu and Longhua Yu
Remote Sens. 2023, 15(14), 3480; https://doi.org/10.3390/rs15143480 - 10 Jul 2023
Cited by 3 | Viewed by 1662
Abstract
Diameter at breast height (DBH) is a critical metric for quantifying forest resources, and obtaining accurate, efficient measurements of DBH is crucial for effective forest management and inventory. A backpack LiDAR system (BLS) can provide high-resolution representations of forest trunk structures, making it [...] Read more.
Diameter at breast height (DBH) is a critical metric for quantifying forest resources, and obtaining accurate, efficient measurements of DBH is crucial for effective forest management and inventory. A backpack LiDAR system (BLS) can provide high-resolution representations of forest trunk structures, making it a promising tool for DBH measurement. However, in practical applications, deep learning-based tree trunk detection and DBH estimation using BLS still faces numerous challenges, such as complex forest BLS data, low proportions of target point clouds leading to imbalanced class segmentation accuracy in deep learning models, and low fitting accuracy and robustness of trunk point cloud DBH methods. To address these issues, this study proposed a novel framework for BLS stratified-coupled tree trunk detection and DBH estimation in forests (BSTDF). This framework employed a stratified coupling approach to create a tree trunk detection deep learning dataset, introduced a weighted cross-entropy focal-loss function module (WCF) and a cosine annealing cyclic learning strategy (CACL) to enhance the WCF-CACL-RandLA-Net model for extracting trunk point clouds, and applied a (least squares adaptive random sample consensus) LSA-RANSAC cylindrical fitting method for DBH estimation. The findings reveal that the dataset based on the stratified-coupled approach effectively reduces the amount of data for deep learning tree trunk detection. To compare the accuracy of BSTDF, synchronous control experiments were conducted using the RandLA-Net model and the RANSAC algorithm. To benchmark the accuracy of BSTDF, we conducted synchronized control experiments utilizing a variety of mainstream tree trunk detection models and DBH fitting methodologies. Especially when juxtaposed with the RandLA-Net model, the WCF-CACL-RandLA-Net model employed by BSTDF demonstrated a 6% increase in trunk segmentation accuracy and a 3% improvement in the F1 score with the same training sample volume. This effectively mitigated class imbalance issues encountered during the segmentation process. Simultaneously, when compared to RANSAC, the LSA-RANCAC method adopted by BSTDF reduced the RMSE by 1.08 cm and boosted R2 by 14%, effectively tackling the inadequacies of RANSAC’s filling. The optimal acquisition distance for BLS data is 20 m, at which BSTDF’s overall tree trunk detection rate (ER) reaches 90.03%, with DBH estimation precision indicating an RMSE of 4.41 cm and R2 of 0.87. This study demonstrated the effectiveness of BSTDF in forest DBH estimation, offering a more efficient solution for forest resource monitoring and quantification, and possessing immense potential to replace field forest measurements. Full article
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<p>Study area: (<b>A</b>) the location of the study area in Jiangxi province; (<b>B</b>) the location of the study area in Fenyi County; (<b>C</b>) the red represents the distribution of trees, and the green dotted line represents the one-way route of LiDAR data acquisition.</p>
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<p>Distribution statistics of tree height and DBH of conifers and broad-leaved trees in the study area: (<b>A</b>) broad-leaved trees; (<b>B</b>) coniferous trees.</p>
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<p>BLS data collection equipment: (<b>A</b>) operation method under the forest; (<b>B</b>) GNNS receiver for enhanced positioning; (<b>C</b>) LiDAR scanner RIEGL miniVUX-1UAV; (<b>D</b>) point cloud in the research area.</p>
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<p>The flowchart of this study.</p>
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<p>Data processing of this study: (<b>A</b>,<b>B</b>,<b>C</b>) preprocessing of data; (<b>D</b>,<b>E</b>,<b>F</b>) stratified and coupled of data; (<b>G</b>) classification of the data set (the red box represents TDS; the green box represents PDS; the yellow box represents VDS).</p>
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<p>The network structure of WCF-CACL-RandLA-Net. (N, D) represents the number and characteristic dimension of points, respectively. FC represents the fully connected layer; LFA represents the local feature aggregation; RS represents the random sampling; MLP represents the shared multi-layer perceptron; US represents the upsampling; DP represents the dropout.</p>
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<p>Schematic diagram of fitting cylindrical space of LSA-RANSAC.</p>
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<p>The training process of two deep learning models: (<b>A</b>) the change process of training accuracy; (<b>B</b>) the training loss change process. Black represents RandLA-Net. The red color in the figure represents WCF-CACL-RandLA-Net.</p>
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<p>Segmentation results using different methods. Orange represents the ground, red represents the Tree-trunk category, and green represents the Shrub-branch category. (<b>A</b>) Point cloud to be segmented after Stratified-Coupled processing; (<b>B</b>,<b>b</b>) Segmentation results based on KPConv [<a href="#B25-remotesensing-15-03480" class="html-bibr">25</a>]; (<b>C</b>,<b>c</b>) segmentation results based on PointNet++ [<a href="#B30-remotesensing-15-03480" class="html-bibr">30</a>]; (<b>D</b>,<b>d</b>) segmentation results based on VF [<a href="#B18-remotesensing-15-03480" class="html-bibr">18</a>]; (<b>E</b>,<b>e</b>) segmentation results based on RandLA-Net [<a href="#B28-remotesensing-15-03480" class="html-bibr">28</a>]; (<b>F</b>,<b>f</b>) segmentation results based on WCF-CACL-RandLA-Net, (<b>G</b>) Research area segmentation results based on WCF-CACL-RandLA-Net.</p>
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<p>Distance level division and tree distribution map for tree trunk detection rate statistics.</p>
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<p>Tree distribution fitting DBH based on LSA-RANCAC.</p>
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<p>Comparison of the accuracy of DBH estimation results for three forest types based on LSA-RANCAC.</p>
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20 pages, 1270 KiB  
Article
Artificial Bee Colony Algorithm with Pareto-Based Approach for Multi-Objective Three-Dimensional Single Container Loading Problems
by Suriya Phongmoo, Komgrit Leksakul, Nivit Charoenchai and Chawis Boonmee
Appl. Sci. 2023, 13(11), 6601; https://doi.org/10.3390/app13116601 - 29 May 2023
Cited by 4 | Viewed by 1723
Abstract
The ongoing container shortage crisis has presented significant challenges for the freight forwarding industry, requiring companies to implement adaptive measures in order to maintain peak operational efficiency. This article presents a novel mathematical model and artificial bee colony algorithm (ABC) with a Pareto-based [...] Read more.
The ongoing container shortage crisis has presented significant challenges for the freight forwarding industry, requiring companies to implement adaptive measures in order to maintain peak operational efficiency. This article presents a novel mathematical model and artificial bee colony algorithm (ABC) with a Pareto-based approach to solve single-container-loading problems. The goal is to fit a set of boxes with strongly heterogeneous boxes into a container with a specific dimension to minimize the broken space and maximize profits. Furthermore, the proposed algorithm incorporates the bottom-left fill method, which is a heuristic strategy for packing containers. We conducted numerical testing to identify optimal parameters using the C~ metric method. Subsequently, we evaluated the performance of our proposed algorithm by comparing it to other heuristics and meta-heuristic approaches using the relative improvement (RI) value. Our analysis showed that our algorithm outperformed the other approaches and achieved the best results. These results demonstrate the effectiveness of the proposed algorithm in solving real-world single-container-loading problems for freight forwarding companies. Full article
(This article belongs to the Special Issue Advanced Artificial Intelligence Theories and Applications)
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<p>Illustration of the Pareto-optimal set of the Pareto-based approach.</p>
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<p>Flowchart of proposed ABC algorithm with Pareto-based approach.</p>
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<p>Roulette wheel selection method.</p>
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19 pages, 11170 KiB  
Article
Spatial Distribution Characteristic and Type Classification of Rural Settlements: A Case Study of Weibei Plain, China
by Yaqiong Duan, Su Chen, Lingda Zhang, Dan Wang, Dongyang Liu and Quanhua Hou
Sustainability 2023, 15(11), 8736; https://doi.org/10.3390/su15118736 - 29 May 2023
Cited by 1 | Viewed by 1748
Abstract
The continuous development of urbanization in China has brought new opportunities to rural settlements but has also led to spatial problems such as disorderly layout and unbalanced morphological structures, and the sustainable development of the countryside faces great challenges. As the core spatial [...] Read more.
The continuous development of urbanization in China has brought new opportunities to rural settlements but has also led to spatial problems such as disorderly layout and unbalanced morphological structures, and the sustainable development of the countryside faces great challenges. As the core spatial carrier of rural settlements, scientific identification of their characteristics and delineation of their types is conducive to the subsequent spatial optimization of rural settlements to promote the coordinated and orderly development of rural areas. In recent years, several studies have explored the characteristics and classification of rural settlements based on single factor influences, but few studies have comprehensively considered them from a multidimensional perspective. To fill this gap, this paper takes the rural settlements in the Weibei Plain as the research object, uses the continuous spectral transect analysis method, combines the landscape security pattern analysis, establishes a multidimensional feature matrix model, quantitatively analyzes the spatial differentiation characteristics, and classifies the types. The key findings are as follows. (1) According to the analysis of landscape security patterns, it was divided into four types of rural settlements. The rural settlements with high and medium security patterns accounted for 86.79%, and the overall ecological adaptability was good. (2) In terms of spatial distribution, 80% of patches in the Weihe River transect are small and unevenly distributed under the influence of river runoff, gradually changing from dense to discrete; the fluctuation range of the 70% patch area is restricted by the terrain in the Hanyuan tableland transect is small and changes from discrete to dense. In terms of spatial morphology, 70% of the Weihe River transect was irregular and varied greatly. The morphology of the Hanyuan tableland transect tended to be similar, and the degree of fragmentation of the Hanyuan tableland transect was higher than that of the Weihe River transect. (3) The Weihe River transect was divided into six types of settlement space, the Hanyuan tableland transect was divided into seven types, and the characteristics of different settlement space types were quite different. The results can provide a scientific basis for the spatial planning, industrial guidance, and facility layout of rural settlements and have important significance for the rational formulation of spatial agglomeration guidance strategies and the promotion of sustainable rural development in China. Full article
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<p>Overall flowchart of the research.</p>
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<p>Regional Scope of Weibei Plain.</p>
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<p>Settlement Distribution and Transect Setting.</p>
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<p>Construction of Suitability-Distribution Form Classification System.</p>
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<p>SDF Characteristic Matrix Model.</p>
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<p>Security Pattern in Weibei Plain. (<b>a</b>) Security Pattern of Hydrology; (<b>b</b>) Security Pattern of Geological Disasters; (<b>c</b>) Security Pattern of Urban Sprawl; (<b>d</b>) Security Pattern of Cultural Heritage; (<b>e</b>) Security Pattern of Recreational Space; (<b>f</b>) Comprehensive Landscape Security Pattern.</p>
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<p>Security Pattern in Weibei Plain. (<b>a</b>) Security Pattern of Hydrology; (<b>b</b>) Security Pattern of Geological Disasters; (<b>c</b>) Security Pattern of Urban Sprawl; (<b>d</b>) Security Pattern of Cultural Heritage; (<b>e</b>) Security Pattern of Recreational Space; (<b>f</b>) Comprehensive Landscape Security Pattern.</p>
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<p>Statistics of WH Transect and HY Transect Index. (<b>a</b>) MPS; (<b>b</b>) PD; (<b>c</b>) MNN; (<b>d</b>) CONNECT; (<b>e</b>) SHAPE-MN; (<b>f</b>) SHDI.</p>
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<p>Zoning of WH Transect.</p>
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<p>Zoning of HY Transect.</p>
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27 pages, 3495 KiB  
Article
Adverse Weather Impacts on Winter Wheat, Maize and Potato Yield Gaps in northern Belgium
by Fien Vanongeval and Anne Gobin
Agronomy 2023, 13(4), 1104; https://doi.org/10.3390/agronomy13041104 - 12 Apr 2023
Cited by 1 | Viewed by 2385
Abstract
Adverse weather conditions greatly reduce crop yields, leading to economic losses and lower food availability. The characterization of adverse weather and the quantification of their potential impact on arable farming is necessary to advise farmers on feasible and effective adaptation strategies and to [...] Read more.
Adverse weather conditions greatly reduce crop yields, leading to economic losses and lower food availability. The characterization of adverse weather and the quantification of their potential impact on arable farming is necessary to advise farmers on feasible and effective adaptation strategies and to support decision making in the agriculture sector. This research aims to analyze the impact of adverse weather on the yield of winter wheat, grain maize and late potato using a yield gap approach. A time-series analysis was performed to identify the relationship between (agro-)meteorological indicators and crop yields and yield gaps in Flanders (northern Belgium) based on 10 years of field trial and weather data. Indicators were calculated for different crop growth stages and multiple soils. Indicators related to high temperature, water deficit and water excess were analyzed, as the occurrence frequency and intensity of these weather events will most likely increase by 2030–2050. The concept of “yield gap” was used to analyze the effects of adverse weather in relation to other yield-reducing factors such as suboptimal management practices. Winter wheat preferred higher temperatures during grain filling and was negatively affected by wet conditions throughout the growing season. Maize was especially vulnerable to drought throughout the growing season. Potato was more affected by heat and drought stress during tuber bulking and by waterlogging during the early growth stages. The impact of adverse weather on crop yield was influenced by soil type, and optimal management practices mitigated the impact of adverse weather. Full article
(This article belongs to the Section Soil and Plant Nutrition)
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<p>Locations of field trials within the agricultural zones of Flanders. Labels w, m and p stand for winter wheat, maize and potato. The major soil textural classes (USDA) are sandy loam in the Campines, silt in the Loam Region, clay loam in the Polder Region and silt loam in the Sandy–Loam Region.</p>
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<p>Definitions of yield levels and yield gap approach used in this study, with potential yield (<span class="html-italic">Y<sub>P</sub></span>), optimal management yield (<span class="html-italic">Y<sub>M</sub></span>) and actual yield (<span class="html-italic">Y<sub>A</sub></span>).</p>
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<p>Cropping calendar for winter wheat, maize and late potato in Belgium.</p>
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<p>Winter wheat yield gaps during the 2011–2021 period: potential yield (<span class="html-italic">Y<sub>P</sub></span>), optimal management yield (<span class="html-italic">Y<sub>M</sub></span>) and actual yield (<span class="html-italic">Y<sub>A</sub></span>). Significant differences (Wilcoxon test; <span class="html-italic">p</span> &lt; 0.05 or <span class="html-italic">p</span> &lt; 0.001) Y<sub>M</sub> on the three soils (yellow), for Y<sub>A</sub> on the three soils (gray) and for the difference between Y<sub>M</sub> and Y<sub>A</sub> for each soil type separately (green, orange and purple) are indicated by a different letter.</p>
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<p>Maize yield gaps during the 2011–2021 period: potential yield (<span class="html-italic">Y<sub>P</sub></span>), optimal management yield (<span class="html-italic">Y<sub>M</sub></span>) and actual yield (<span class="html-italic">Y<sub>A</sub></span>). Significant differences (Wilcoxon test; <span class="html-italic">p</span> &lt; 0.05 or <span class="html-italic">p</span> &lt; 0.001) Y<sub>M</sub> on the three soils (yellow), for Y<sub>A</sub> on the three soils (gray) and for the difference between Y<sub>M</sub> and Y<sub>A</sub> for each soil type separately (green, orange and purple) are indicated by a different letter.</p>
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<p>Potato yield gaps during the 2011–2021 period: potential yield (<span class="html-italic">Y<sub>P</sub></span>), optimal management yield (<span class="html-italic">Y<sub>M</sub></span>) and actual yield (<span class="html-italic">Y<sub>A</sub></span>). Significant differences (Wilcoxon test; <span class="html-italic">p</span> &lt; 0.05 or <span class="html-italic">p</span> &lt; 0.001) Y<sub>M</sub> on the two soils (yellow), for Y<sub>A</sub> on the two soils (gray) and for the difference between Y<sub>M</sub> and Y<sub>A</sub> for each soil type separately (green and orange) are indicated by a different letter.</p>
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<p>Correlation matrix (Pearson’s) for winter wheat with potential yield (<span class="html-italic">Y<sub>M</sub></span>), optimal management yield (<span class="html-italic">Y<sub>M</sub></span>) and actual yield (<span class="html-italic">Y<sub>A</sub></span>). Heat stress index (<span class="html-italic">HSI</span>), precipitation deficit index (<span class="html-italic">PDI</span>), water deficit index (<span class="html-italic">WDI</span>) and waterlogging index (<span class="html-italic">WLI</span>) for emergence (<span class="html-italic">S1</span>), vegetative growth (<span class="html-italic">S2</span>), flowering (<span class="html-italic">S3</span>) and grain filling and ripening (<span class="html-italic">S4</span>). Darker blue colors indicate more positive correlation and darker red colors indicate more negative correlation.</p>
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<p>Correlation matrix (Pearson’s) for maize with potential yield (<span class="html-italic">Y<sub>P</sub></span>) optimal management yield (<span class="html-italic">Y<sub>M</sub></span>) and actual yield (<span class="html-italic">Y<sub>A</sub></span>). Heat stress index (<span class="html-italic">HSI</span>), precipitation deficit index (<span class="html-italic">PDI</span>), water deficit index (<span class="html-italic">WDI</span>) and waterlogging index (<span class="html-italic">WLI</span>) for emergence (<span class="html-italic">S1</span>), vegetative growth (<span class="html-italic">S2</span>), flowering (<span class="html-italic">S3</span>) and grain filling and ripening (<span class="html-italic">S4</span>). Darker blue colors indicate more positive correlation and darker red colors indicate more negative correlation.</p>
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<p>Correlation matrix (Pearson’s) for potato with potential yield (<span class="html-italic">Y<sub>P</sub></span>) optimal management yield (<span class="html-italic">Y<sub>M</sub></span>) and actual yield (<span class="html-italic">Y<sub>A</sub></span>). Heat stress index (<span class="html-italic">HSI</span>), precipitation deficit index (<span class="html-italic">PDI</span>), water deficit index (<span class="html-italic">WDI</span>) and waterlogging index (<span class="html-italic">WLI</span>) for emergence (<span class="html-italic">S1</span>), vegetative growth (<span class="html-italic">S2</span>), tuber set (<span class="html-italic">S3</span>) and tuber bulking (<span class="html-italic">S4</span>). Darker blue colors indicate more positive correlation and darker red colors indicate more negative correlation.</p>
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