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Search Results (3,180)

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34 pages, 4757 KiB  
Article
Electrical Storm Optimization (ESO) Algorithm: Theoretical Foundations, Analysis, and Application to Engineering Problems
by Manuel Soto Calvo and Han Soo Lee
Mach. Learn. Knowl. Extr. 2025, 7(1), 24; https://doi.org/10.3390/make7010024 - 6 Mar 2025
Abstract
The electrical storm optimization (ESO) algorithm, inspired by the dynamic nature of electrical storms, is a novel population-based metaheuristic that employs three dynamically adjusted parameters: field resistance, field intensity, and field conductivity. Field resistance assesses the spread of solutions within the search space, [...] Read more.
The electrical storm optimization (ESO) algorithm, inspired by the dynamic nature of electrical storms, is a novel population-based metaheuristic that employs three dynamically adjusted parameters: field resistance, field intensity, and field conductivity. Field resistance assesses the spread of solutions within the search space, reflecting strategy diversity. The field intensity balances the exploration of new territories and the exploitation of promising areas. The field conductivity adjusts the adaptability of the search process, enhancing the algorithm’s ability to escape local optima and converge on global solutions. These adjustments enable the ESO to adapt in real-time to various optimization scenarios, steering the search toward potential optima. ESO’s performance was rigorously tested against 60 benchmark problems from the IEEE CEC SOBC 2022 suite and 20 well-known metaheuristics. The results demonstrate the superior performance of ESOs, particularly in tasks requiring a nuanced balance between exploration and exploitation. Its efficacy is further validated through successful applications in four engineering domains, highlighting its precision, stability, flexibility, and efficiency. Additionally, the algorithm’s computational costs were evaluated in terms of the number of function evaluations and computational overhead, reinforcing its status as a standout choice in the metaheuristic field. Full article
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Figure 1
<p>Flowchart of the electrical storm optimization (ESO) algorithm illustrating the initialization of agents, the iterative adjustments of environmental parameters, and the continuous selection and refinement of solutions toward identifying the optimum.</p>
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<p>Conceptual behavior of field intensity curves under different scenarios, showing the dynamic modulation of the transition between the exploration and exploitation stages.</p>
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<p>Convergence curves of the algorithms for unimodal problems. The ESO (red line) shows consistent convergence and MFO (pink line) shows the highest performance variability.</p>
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<p>Convergence curves of the algorithms for multimodal problems. The ESO (red line) shows consistent convergence, whereas the MFO (pink line) and PSO (orange line) show greater performance variability.</p>
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<p>Normalized behavior of field resistance, field conductivity, field intensity, storm power, and progression toward the global best solution over 1000 iterations for benchmark functions F6, F20, F24, F33, F46, and F50.</p>
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<p>Statistical results for the three groups of functions. The critical difference diagrams (<b>A</b>–<b>D</b>) illustrate the relative rankings of the algorithms, highlighting the groups of algorithms that are not significantly different from each other. The heatmaps (<b>A1</b>–<b>D1</b>) show that the Bayesian probability of one algorithm outperforms the other.</p>
Full article ">Figure 6 Cont.
<p>Statistical results for the three groups of functions. The critical difference diagrams (<b>A</b>–<b>D</b>) illustrate the relative rankings of the algorithms, highlighting the groups of algorithms that are not significantly different from each other. The heatmaps (<b>A1</b>–<b>D1</b>) show that the Bayesian probability of one algorithm outperforms the other.</p>
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20 pages, 8921 KiB  
Article
A Survey of IEEE 802.11ax WLAN Temporal Duty Cycle for the Assessment of RF Electromagnetic Exposure
by Yizhen Yang, Günter Vermeeren, Leen Verloock, Mònica Guxens and Wout Joseph
Appl. Sci. 2025, 15(5), 2858; https://doi.org/10.3390/app15052858 - 6 Mar 2025
Abstract
The increasing deployment of IEEE 802.11ax (Wi-Fi 6) networks necessitates an accurate assessment of radiofrequency electromagnetic field (RF-EMF) exposure under realistic usage scenarios. This study investigates the duty cycle (DC) and corresponding exposure levels of Wi-Fi 6 in controlled laboratory conditions, focusing on [...] Read more.
The increasing deployment of IEEE 802.11ax (Wi-Fi 6) networks necessitates an accurate assessment of radiofrequency electromagnetic field (RF-EMF) exposure under realistic usage scenarios. This study investigates the duty cycle (DC) and corresponding exposure levels of Wi-Fi 6 in controlled laboratory conditions, focusing on bandwidth variations, multi-user scenarios, and application types. DC measurements reveal significant variability across internet services, with FTP upload exhibiting the highest mean DC (94.3%) under 20 MHz bandwidth, while YouTube 4K video streaming showed bursts with a maximum DC of 89.2%. Under poor radio conditions, DC increased by up to 5× for certain applications, emphasizing the influence of degraded signal-to-noise ratio (SNR) on retransmissions and modulation. Weighted exposure results indicate a reduction in average electric-field strength by up to 10× when incorporating DC, with maximum weighted exposure at 4.2 V/m (6.9% of ICNIRP limits) during multi-user scenarios. These findings highlight the critical role of realistic DC assessments in refining exposure evaluations, ensuring regulatory compliance, and advancing the understanding of Wi-Fi 6’s EMF exposure implications. Full article
(This article belongs to the Special Issue Electromagnetic Radiation and Human Environment)
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Figure 1
<p>The measurement setup and layout for the single-user scenario. (<b>a</b>) Three-axis antenna was placed at the UD side. (<b>b</b>) Three-axis antenna was placed at the AP side. (<b>c</b>) The overall layout of the measurement setup, and the three-axis antenna was placed at the center.</p>
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<p>Wi-Fi 6 signal recorded using the SA’s zero-span mode.</p>
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<p>The setup for Wi-Fi 6 DC measurements under poor radio conditions, where UD is a laptop.</p>
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<p>Layout of UDs (including a laptop, a mobile phone, a tablet and a laptop with UWiA installed), measurement points (center) and the AP for assessing the exposure level of Wi-Fi 6 in a multi-user scenario (The brown boxes show tables where devices were placed).</p>
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<p>Wi-Fi DC versus time for different activities under 80 MHz bandwidth (YouTube 4K video, FTP download, WhatsApp video call, and web browsing).</p>
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<p>One-second-averaged DCs as a function of Internet application per bandwidth: (<b>a</b>) 20 MHz, (<b>b</b>) 40 MHz, (<b>c</b>) 80 MHz, and (<b>d</b>) 160 MHz. The mean DC for each application over 6 min (marked with a star in the box plot) is labeled above each box.</p>
Full article ">Figure 6 Cont.
<p>One-second-averaged DCs as a function of Internet application per bandwidth: (<b>a</b>) 20 MHz, (<b>b</b>) 40 MHz, (<b>c</b>) 80 MHz, and (<b>d</b>) 160 MHz. The mean DC for each application over 6 min (marked with a star in the box plot) is labeled above each box.</p>
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<p>The comparison of Wi-Fi 6 DCs for different Internet applications under good and poor radio conditions (DC mean values are marked as green triangles).</p>
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<p>DC as a function of the number of UDs for four different Wi-Fi 6 network applications, including 4K video streaming, FTP downloads, web browsing, and video calls (DC mean values are marked as green triangles).</p>
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<p>DC variation over time for 4K video streaming in single-user and four UDs scenarios.</p>
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<p>Comparison of DC distributions for four UDs using different applications simultaneously (“All applications”) versus the same application (DC mean values are marked as green triangles).</p>
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<p>Measured exposure levels (weighted with different DC: <math display="inline"><semantics> <msub> <mi mathvariant="normal">DC</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi mathvariant="normal">DC</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math>, video call, and DC = 100%) at the AP side, UD side, and the center location under varying bandwidths (20 MHz, 40 MHz, 80 MHz, and 160 MHz).</p>
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<p>Measured exposure levels (weighted with different DC: <math display="inline"><semantics> <msub> <mi mathvariant="normal">DC</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi mathvariant="normal">DC</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </semantics></math>, video call and DC = 100%) for different types of UD (laptop, mobile phone, tablet and UWiA) under a bandwidth of 80 MHz.</p>
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<p>Exposure levels at different UDs (laptop, mobile phone, tablet, and UWiA), center, and AP measured in the multi-user scenario for different DCs (all 4 UD-scenario DCs).</p>
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19 pages, 1463 KiB  
Systematic Review
Exploring the Role of Artificial Intelligence (AI)-Driven Training in Laparoscopic Suturing: A Systematic Review of Skills Mastery, Retention, and Clinical Performance in Surgical Education
by Chidozie N. Ogbonnaya, Shizhou Li, Changshi Tang, Baobing Zhang, Paul Sullivan, Mustafa Suphi Erden and Benjie Tang
Healthcare 2025, 13(5), 571; https://doi.org/10.3390/healthcare13050571 - 6 Mar 2025
Viewed by 62
Abstract
Background: Artificial Intelligence (AI)-driven training systems are becoming increasingly important in surgical education, particularly in the context of laparoscopic suturing. This systematic review aims to assess the impact of AI on skill acquisition, long-term retention, and clinical performance, with a specific focus on [...] Read more.
Background: Artificial Intelligence (AI)-driven training systems are becoming increasingly important in surgical education, particularly in the context of laparoscopic suturing. This systematic review aims to assess the impact of AI on skill acquisition, long-term retention, and clinical performance, with a specific focus on the types of machine learning (ML) techniques applied to laparoscopic suturing training and their associated advantages and limitations. Methods: A comprehensive search was conducted across multiple databases, including PubMed, IEEE Xplore, Cochrane Library, and ScienceDirect, for studies published between 2005 and 2024. Following the PRISMA guidelines, 1200 articles were initially screened, and 33 studies met the inclusion criteria. This review specifically focuses on ML techniques such as deep learning, motion capture, and video segmentation and their application in laparoscopic suturing training. The quality of the included studies was assessed, considering factors such as sample size, follow-up duration, and potential biases. Results: AI-based training systems have shown notable improvements in the laparoscopic suturing process, offering clear advantages over traditional methods. These systems enhance precision, efficiency, and long-term retention of key suturing skills. The use of personalized feedback and real-time performance tracking allows learners to gain proficiency more rapidly and ensures that skills are retained over time. These technologies are particularly beneficial for novice surgeons and provide valuable support in resource-limited settings, where access to expert instructors and advanced equipment may be scarce. Key machine learning techniques, including deep learning, motion capture, and video segmentation, have significantly improved specific suturing tasks, such as needle manipulation, insertion techniques, knot tying, and grip control, all of which are critical to mastering laparoscopic suturing. Conclusions: AI-driven training tools are reshaping laparoscopic suturing education by improving skill acquisition, providing real-time feedback, and enhancing long-term retention. Deep learning, motion capture, and video segmentation techniques have proven most effective in refining suturing tasks such as needle manipulation and knot tying. While AI offers significant advantages, limitations in accuracy, scalability, and integration remain. Further research, particularly large-scale, high-quality studies, is necessary to refine these tools and ensure their effective implementation in real-world clinical settings. Full article
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<p>PRISMA flow diagram of study selection.</p>
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<p>Risk of bias assessment for all 33 studies [<a href="#B18-healthcare-13-00571" class="html-bibr">18</a>,<a href="#B23-healthcare-13-00571" class="html-bibr">23</a>,<a href="#B24-healthcare-13-00571" class="html-bibr">24</a>,<a href="#B25-healthcare-13-00571" class="html-bibr">25</a>,<a href="#B26-healthcare-13-00571" class="html-bibr">26</a>,<a href="#B27-healthcare-13-00571" class="html-bibr">27</a>,<a href="#B28-healthcare-13-00571" class="html-bibr">28</a>,<a href="#B29-healthcare-13-00571" class="html-bibr">29</a>,<a href="#B30-healthcare-13-00571" class="html-bibr">30</a>,<a href="#B31-healthcare-13-00571" class="html-bibr">31</a>,<a href="#B32-healthcare-13-00571" class="html-bibr">32</a>,<a href="#B33-healthcare-13-00571" class="html-bibr">33</a>,<a href="#B34-healthcare-13-00571" class="html-bibr">34</a>,<a href="#B35-healthcare-13-00571" class="html-bibr">35</a>,<a href="#B36-healthcare-13-00571" class="html-bibr">36</a>,<a href="#B37-healthcare-13-00571" class="html-bibr">37</a>,<a href="#B38-healthcare-13-00571" class="html-bibr">38</a>,<a href="#B39-healthcare-13-00571" class="html-bibr">39</a>,<a href="#B40-healthcare-13-00571" class="html-bibr">40</a>,<a href="#B41-healthcare-13-00571" class="html-bibr">41</a>,<a href="#B42-healthcare-13-00571" class="html-bibr">42</a>,<a href="#B43-healthcare-13-00571" class="html-bibr">43</a>,<a href="#B44-healthcare-13-00571" class="html-bibr">44</a>,<a href="#B45-healthcare-13-00571" class="html-bibr">45</a>,<a href="#B46-healthcare-13-00571" class="html-bibr">46</a>,<a href="#B47-healthcare-13-00571" class="html-bibr">47</a>,<a href="#B48-healthcare-13-00571" class="html-bibr">48</a>,<a href="#B49-healthcare-13-00571" class="html-bibr">49</a>,<a href="#B50-healthcare-13-00571" class="html-bibr">50</a>,<a href="#B51-healthcare-13-00571" class="html-bibr">51</a>,<a href="#B52-healthcare-13-00571" class="html-bibr">52</a>,<a href="#B53-healthcare-13-00571" class="html-bibr">53</a>,<a href="#B54-healthcare-13-00571" class="html-bibr">54</a>].</p>
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<p>Summary of risk of bias across bias domains [<a href="#B18-healthcare-13-00571" class="html-bibr">18</a>,<a href="#B23-healthcare-13-00571" class="html-bibr">23</a>,<a href="#B24-healthcare-13-00571" class="html-bibr">24</a>,<a href="#B25-healthcare-13-00571" class="html-bibr">25</a>,<a href="#B26-healthcare-13-00571" class="html-bibr">26</a>,<a href="#B27-healthcare-13-00571" class="html-bibr">27</a>,<a href="#B28-healthcare-13-00571" class="html-bibr">28</a>,<a href="#B29-healthcare-13-00571" class="html-bibr">29</a>,<a href="#B30-healthcare-13-00571" class="html-bibr">30</a>,<a href="#B31-healthcare-13-00571" class="html-bibr">31</a>,<a href="#B32-healthcare-13-00571" class="html-bibr">32</a>,<a href="#B33-healthcare-13-00571" class="html-bibr">33</a>,<a href="#B34-healthcare-13-00571" class="html-bibr">34</a>,<a href="#B35-healthcare-13-00571" class="html-bibr">35</a>,<a href="#B36-healthcare-13-00571" class="html-bibr">36</a>,<a href="#B37-healthcare-13-00571" class="html-bibr">37</a>,<a href="#B38-healthcare-13-00571" class="html-bibr">38</a>,<a href="#B39-healthcare-13-00571" class="html-bibr">39</a>,<a href="#B40-healthcare-13-00571" class="html-bibr">40</a>,<a href="#B41-healthcare-13-00571" class="html-bibr">41</a>,<a href="#B42-healthcare-13-00571" class="html-bibr">42</a>,<a href="#B43-healthcare-13-00571" class="html-bibr">43</a>,<a href="#B44-healthcare-13-00571" class="html-bibr">44</a>,<a href="#B45-healthcare-13-00571" class="html-bibr">45</a>,<a href="#B46-healthcare-13-00571" class="html-bibr">46</a>,<a href="#B47-healthcare-13-00571" class="html-bibr">47</a>,<a href="#B48-healthcare-13-00571" class="html-bibr">48</a>,<a href="#B49-healthcare-13-00571" class="html-bibr">49</a>,<a href="#B50-healthcare-13-00571" class="html-bibr">50</a>,<a href="#B51-healthcare-13-00571" class="html-bibr">51</a>,<a href="#B52-healthcare-13-00571" class="html-bibr">52</a>,<a href="#B53-healthcare-13-00571" class="html-bibr">53</a>,<a href="#B54-healthcare-13-00571" class="html-bibr">54</a>].</p>
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27 pages, 6606 KiB  
Article
Dynamic Bayesian Network Model for Overhead Power Lines Affected by Hurricanes
by Kehkashan Fatima and Hussain Shareef
Forecasting 2025, 7(1), 11; https://doi.org/10.3390/forecast7010011 - 5 Mar 2025
Viewed by 338
Abstract
This paper investigates the dynamics of Hurricane-Induced Failure (HIF) by developing a probabilistic framework using a Dynamic Bayesian Network (DBN) model. The model captures the complex interplay of factors influencing Hurricane Wind Speed Intensity (HWSI) and its impact on asset failures. In the [...] Read more.
This paper investigates the dynamics of Hurricane-Induced Failure (HIF) by developing a probabilistic framework using a Dynamic Bayesian Network (DBN) model. The model captures the complex interplay of factors influencing Hurricane Wind Speed Intensity (HWSI) and its impact on asset failures. In the proposed DBN model, the pole failure mechanism is represented using Bayesian probabilistic principles, encompassing bending elasticity endurance and the foundational strength of the system poles. To characterize the stochastic properties of HIF, Monte Carlo simulation (MCS) is employed in conjunction with fragility curves (FC) and the scenario reduction (SCENRED) algorithm. The proposed DBN model evaluates the probability of asset failure and compares the results using stochastic Monte Carlo simulation based on the fragility curve scenario reduction algorithm (FC-MCS-SCENRED) model. The results are validated on a standard IEEE 15 bus and IEEE 33 bus radial distribution system as a case study. The DBN results show that they are consistent with the data obtained using the FC-MCS-SCENRED model. The results also reveal that the HWSI plays a critical role in determining HIF rates and the likelihood of asset failures. These findings hold significant implications for the inspection and maintenance scheduling of distribution overhead power lines susceptible to hurricane-induced impacts. Full article
(This article belongs to the Section Power and Energy Forecasting)
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<p>POP exploiting various categories of (<b>a</b>) modern learning approach (<b>b</b>) machine learning algorithms [<a href="#B31-forecasting-07-00011" class="html-bibr">31</a>].</p>
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<p>A static BN showing the root node (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">X</mi> <mn>1</mn> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math>, the intermediate nodes (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">X</mi> <mn>2</mn> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">X</mi> <mn>3</mn> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>), and the leaf node (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">X</mi> <mn>4</mn> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math>).</p>
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<p>A graphical representation of a DBN over N time slices.</p>
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<p>Flowchart for K-means SCENRED technique.</p>
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<p>The standard radial test distribution system: (<b>a</b>) IEEE 15 bus and (<b>b</b>) IEEE 33 bus.</p>
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<p>An illustrative representation of the methodology used in the case study.</p>
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<p>The structure of the BN overhead line outage prediction model: (<b>a</b>) IEEE 15 bus system and (<b>b</b>) IEEE 33 bus system.</p>
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<p>The structure of the BN overhead line outage prediction model: (<b>a</b>) IEEE 15 bus system and (<b>b</b>) IEEE 33 bus system.</p>
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<p>Flowchart for FC-MCS-SCENRED technique.</p>
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<p>Flowchart for determining failure probability of overhead system line using DBN.</p>
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<p>DBN simulation model for IEEE 15 bus overhead <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">L</mi> </mrow> </semantics></math> failure.</p>
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<p>Dynamic FP of each <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">L</mi> </mrow> </semantics></math> for different HWSIs over 5 time slices for IEEE 15 bus system.</p>
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<p>Dynamic FP of each <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">L</mi> </mrow> </semantics></math> for same HWSI over 5 time slices.</p>
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<p>The sensitivity analysis—the impact of <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">L</mi> <mn>1</mn> </mrow> </semantics></math> on the consecutive system lines of the IEEE 15 bus system.</p>
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<p>Wind pressure on conductors of IEEE bus system for different wind attack angles and HWSI.</p>
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<p>Regional set up: IEEE 33 bus radial distribution system.</p>
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<p>DBN simulation model for IEEE 33 bus overhead <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">L</mi> </mrow> </semantics></math> failure.</p>
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<p>Dynamic FP of each <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">L</mi> </mrow> </semantics></math> for different HWSI over 5 time slices for IEEE 33 bus system.</p>
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<p>The sensitivity analysis—the impact of <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">L</mi> <mn>1</mn> </mrow> </semantics></math> on the consecutive system lines of the IEEE 33 bus system.</p>
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<p>Wind pressure on conductors of the IEEE 33 bus system for different wind attack angles and HWSIs.</p>
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<p>Damage scenarios of FC-MCS-SCENRED model for IEEE 15 bus system.</p>
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<p>Damage scenarios of FC-MCS-SCENRED model for IEEE 33 bus system.</p>
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<p>SL FP using DBN and FC-MCS-SCENRED for different HWSI: (<b>a</b>) IEEE 15 bus system and (<b>b</b>) IEEE 33 bus system.</p>
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<p>The graphical representation of the line faults on standard radial distribution systems: the (<b>a</b>) IEEE 15 bus system and (<b>b</b>) IEEE 33 bus system.</p>
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16 pages, 3392 KiB  
Article
Voltage Stability Estimation Considering Variability in Reactive Power Reserves Using Regression Trees
by Masato Miyazaki, Mutsumi Aoki and Yuta Nakamura
Energies 2025, 18(5), 1260; https://doi.org/10.3390/en18051260 - 4 Mar 2025
Viewed by 193
Abstract
The rapid integration of renewable energy sources, such as photovoltaic power systems, has reduced the necessary for synchronous generators, which traditionally contributed to grid stability during disturbances. This shift has led to a decrease in reactive power reserves (RPRs), raising concerns about voltage [...] Read more.
The rapid integration of renewable energy sources, such as photovoltaic power systems, has reduced the necessary for synchronous generators, which traditionally contributed to grid stability during disturbances. This shift has led to a decrease in reactive power reserves (RPRs), raising concerns about voltage stability. Real-time monitoring of voltage stability is crucial for transmission system operators to implement timely corrective actions. However, conventional methods, such as continuation power flow calculations, are computationally intensive and unsuitable for large-scale power systems. Machine learning techniques using data from phasor measurement units have been proposed to estimate voltage stability. However, these methods do not consider changes in generator operating conditions and fluctuating RPRs. As renewable energy generation increases, the operating conditions of generators vary, which leads to significant changes in system RPRs and voltage stability. In this paper, a voltage stability margin is proposed using regression trees with RPRs varying based on generator operation conditions. Simulations based on the IEEE 9-bus system demonstrate that the proposed approach provides an accurate and efficient voltage stability estimation. Full article
(This article belongs to the Section F3: Power Electronics)
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<p><span class="html-italic">P–V</span> curve.</p>
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<p>Capability curve of a synchronous generator.</p>
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<p>Test system for voltage stability assessment.</p>
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<p>CPF results with varying RPRs: (<b>a</b>) <span class="html-italic">P–V</span> curves; (<b>b</b>) reactive power output of a synchronous generator without limitation.</p>
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<p>Flowchart for the creation of the estimation models.</p>
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<p>Test system.</p>
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<p>Inputs and outputs of the estimation model [<a href="#B38-energies-18-01260" class="html-bibr">38</a>].</p>
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<p>Assessment of the impact of varying reactive power supply limitations: (<b>a</b>) RMSE; (<b>b</b>) maximum error [<a href="#B38-energies-18-01260" class="html-bibr">38</a>].</p>
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<p>Overall framework of the proposed method.</p>
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<p>Effect of the number of segments.</p>
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<p>Comparison of results by the proposed method: (<b>a</b>) RMSE; (<b>b</b>) maximum error.</p>
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<p>Effectiveness verification of the proposed method: (<b>a</b>) RMSE; (<b>b</b>) maximum error.</p>
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<p>Comparison of the results of the estimation models for the proposed method and Method 2: (<b>a</b>) RMSE; (<b>b</b>) maximum error.</p>
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30 pages, 5168 KiB  
Review
Twenty-Five Years of Scientific Production on Geoparks from the Perspective of Bibliometric Analysis Using PRISMA
by Judith Nyulas, Ștefan Dezsi, Adrian-Florin Niță, Zsolt Magyari-Sáska, Marie-Luise Frey and Alpár Horváth
Sustainability 2025, 17(5), 2218; https://doi.org/10.3390/su17052218 - 4 Mar 2025
Viewed by 232
Abstract
Over the last 25 years, research on geoparks has moved from basic research to comprehensive multidisciplinary studies related to the creation and development of geoparks, integrating the principle of sustainability. This research focuses on exploring geoparks as the core subject. The aim of [...] Read more.
Over the last 25 years, research on geoparks has moved from basic research to comprehensive multidisciplinary studies related to the creation and development of geoparks, integrating the principle of sustainability. This research focuses on exploring geoparks as the core subject. The aim of this study is to synthesize the heterogeneous body of knowledge about geoparks in an exhaustive way by leveraging a multi-database bibliometric approach. The methodology applied is based on quantitative bibliometric analysis using R, including its application for non-coders and ensuring reliability with the PRISMA Statement framework. Ten databases were taken as the sources of research papers: Web of Science, Scopus, PubMed, Nature Journals, SpringerLink, Taylor & Francis, Wiley Journals, IEEE Xplore, and CABI. The method we used has limitations, providing a restricted number of trends aligned and scaled to the database boundary conditions used in analysis. The main goals of quantitative bibliometric analysis are as follows: (1) The impact of data integration—Evaluating how merging the data from the ten databases improves research coverage. (2) Global research trends—Identifying the evolution of geopark-related studies over time. (3) Three-year forecast—Predicting the upcoming research directions using a polynomial regression model. (4) Academic performance—Assessing geographical distribution, citation impact, and productivity using bibliometric laws. (5) Conceptual contribution—Identifying the key research themes that drive future studies and potential areas for exploration. Among these, we highlighted the key elements. The integration of the ten databases provides 63% greater insight into scientific research compared to that of the Web of Science (WoS) database. Geographically, the scientific output spans 102 countries, with China leading in production over the last two decades. The most impactful paper has accumulated 768 citations, while Ruben D.A. and Wu Fandong emerge as the most prolific authors. According to the bibliometric law, the core source of scientific output is Geoheritage. The future research directions are expected to address global challenges, particularly natural disasters in alignment with the Sustainable Development Goals (SDGs). Additionally, GIS-based subtopics leveraging advanced technologies for analyzing, mapping, and promoting geological resources represent a promising area for further exploration. The projections indicate that by the end of 2026, scientific production in this field could reach 5226 published papers, underscoring the growing significance of geopark research and interdisciplinary advancements. Full article
(This article belongs to the Special Issue GeoHeritage and Geodiversity in the Natural Heritage: Geoparks)
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<p>Prisma 2020 flow diagram adapted for bibliometric analysis. Source: Page MJ, et al. BMJ 2021 [<a href="#B48-sustainability-17-02218" class="html-bibr">48</a>].</p>
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<p>Annual scientific production and its worldwide distribution (by authors’ country of affiliation).</p>
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<p>Geographic distribution analysis into two time periods: (<b>left</b>). 1999–2011 (early research contributions) and (<b>right</b>). 2012–2024 (by authors’ country of affiliation).</p>
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<p>Average citations per year.</p>
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<p>Evolution of R<sup>2</sup> and RMSE for different degree polynomial models.</p>
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<p>Best-fitting third-degree polynomial regression curve and estimated values for 2024–2026 (3-year forecast growth).</p>
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<p>Author productivity as shown through Lotka’s law. The X-axis measures productivity; the Y-axis shows the proportion of authors contributing to a given number of papers. The graphical output was generated using the Bibliometrix package in R.</p>
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<p>Core sources according to Bradford’s Law.</p>
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<p>A strategic map of geopark research. The size of the bubbles indicates the number of documents with related terms clustered in groups A, B, C, D, E, and F.</p>
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15 pages, 1791 KiB  
Article
Optimal Allocation of Phasor Measurement Units Using Particle Swarm Optimization: An Electric Grid Planning Perspective
by Mohammed Haj-ahmed, Mais M. Aldwaik and Dia Abualnadi
Energies 2025, 18(5), 1225; https://doi.org/10.3390/en18051225 - 3 Mar 2025
Viewed by 118
Abstract
In this paper, the particle swarm optimization (PSO) technique is used to optimally allocate phasor measurement units (PMUs) within standard test systems and a real-world power system. PMUs are allocated at system substations in a manner that ensures complete system observability while minimizing [...] Read more.
In this paper, the particle swarm optimization (PSO) technique is used to optimally allocate phasor measurement units (PMUs) within standard test systems and a real-world power system. PMUs are allocated at system substations in a manner that ensures complete system observability while minimizing installation costs. This study considers IEEE 14-, 30-, and 57-bus standard test systems, along with the Jordanian national high-voltage grid. The optimal allocation was performed separately on the 132 kV and 400 kV buses of the Jordanian grid. Additionally, a novel technique for further minimization of measurement units, considering electric grid planning, is investigated. The results demonstrate that the proposed approach successfully reduces the required number of PMUs while maintaining full system observability. For instance, the IEEE 14-bus system achieved complete observability with only four PMUs, while the IEEE 30-bus and 57-bus systems required ten and seventeen PMUs, respectively. For the Jordanian transmission network, the 400 kV system required only three PMUs, and the 132 kV system required twenty-six PMUs. Furthermore, it was found that integrating power system planning and grid expansion strategies into the PMU placement problem may further reduce installation costs. The results emphasize the effectiveness of the proposed approach in enhancing situational awareness, improving state estimation accuracy, and facilitating reliable protection, control, and monitoring schemes. This study concludes that an optimal PMU allocation strategy shall be incorporated into power system planning studies to maximize cost efficiency while ensuring full observability. Full article
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<p>Fitness error for the 87-bus 132 kV system.</p>
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<p>Graphical illustration of system expansion. (The numbers indicate the bus numbers, the red dotted line is the future lines, and the question marks represent which decision shall be taken).</p>
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<p>Graphical illustration of system reconfiguration on bus 8. (The numbers indicate the bus numbers, the red dotted line is the future lines, and the question marks represent which decision shall be taken).</p>
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<p>Substations connection algorithm.</p>
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31 pages, 4379 KiB  
Systematic Review
A Systematic Literature Review of the Latest Advancements in XAI
by Zaid M. Altukhi, Sojen Pradhan and Nasser Aljohani
Technologies 2025, 13(3), 93; https://doi.org/10.3390/technologies13030093 - 1 Mar 2025
Viewed by 349
Abstract
This systematic review details recent advancements in the field of Explainable Artificial Intelligence (XAI) from 2014 to 2024. XAI utilises a wide range of frameworks, techniques, and methods used to interpret machine learning (ML) black-box models. We aim to understand the technical advancements [...] Read more.
This systematic review details recent advancements in the field of Explainable Artificial Intelligence (XAI) from 2014 to 2024. XAI utilises a wide range of frameworks, techniques, and methods used to interpret machine learning (ML) black-box models. We aim to understand the technical advancements in the field and future directions. We followed the PRISMA methodology and selected 30 relevant publications from three main databases: IEEE Xplore, ACM, and ScienceDirect. Through comprehensive thematic analysis, we categorised the research into three main topics: ‘model developments’, ‘evaluation metrics and methods’, and ‘user-centred and XAI system design’. Our results uncover ‘What’, ‘How’, and ‘Why’ these advancements were developed. We found that 13 papers focused on model developments, 8 studies focused on the XAI evaluation metrics, and 12 papers focused on user-centred and XAI system design. Moreover, it was found that these advancements aimed to bridge the gap between technical model outputs and user understanding. Full article
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<p>XAI framework process flow chart. Adapted from [<a href="#B9-technologies-13-00093" class="html-bibr">9</a>].</p>
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<p>Distribution of publications and databases.</p>
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<p>PRISMA flow diagram of paper selection. Created using [<a href="#B27-technologies-13-00093" class="html-bibr">27</a>].</p>
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<p>Number of articles within each category.</p>
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<p>XAI advancements categories across the 30 articles (five studies cover more than one category, as shown in <a href="#technologies-13-00093-t004" class="html-table">Table 4</a>).</p>
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<p>Flowchart for understanding how black-box algorithms work (What) by identifying the factors influencing their outputs (How) and their human or technical considerations (Why).</p>
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<p>Flowchart of the process of understanding XAI explanations (What) through diverse methods (How), and their goals (Why).</p>
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<p>Flowchart of the process of improving model performance (What) through specific techniques (How), to increase AI transparency and interpretability (Why).</p>
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<p>Flowchart of XAI evaluation articles (What) through various methods (How), to assess the effectiveness of XAI explanations and systems (Why).</p>
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<p>Flowchart on user-centred conceptual frameworks (What) devised through a variety of research approaches (How) to optimise XAI processes (Why).</p>
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<p>Flowchart of XAI system design guidelines (What) outlined by developing frameworks and guidelines (How), with goals to prioritise user needs, make XAI systems accessible to non-expert users, and help developers select the most appropriate methods (Why).</p>
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<p>Flowchart of XAI methods (What) that utilise technical features (How) to optimise XAI processes (Why).</p>
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<p>Flowchart of XAI solutions (What) that consider users and enable technical features (How) to expand the accessibility of solutions for a wider range of users (Why).</p>
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21 pages, 1182 KiB  
Review
Advancements and Challenges of Visible Light Communication in Intelligent Transportation Systems: A Comprehensive Review
by Prokash Sikder, M. T. Rahman and A. S. M. Bakibillah
Photonics 2025, 12(3), 225; https://doi.org/10.3390/photonics12030225 - 28 Feb 2025
Viewed by 456
Abstract
Visible Light Communication (VLC) has the potential to advance Intelligent Transportation Systems (ITS). This study explores the current advancements of VLC in ITS applications that may enhance traffic flow, road safety, and vehicular communication performance. The potential, benefits, and current research trends of [...] Read more.
Visible Light Communication (VLC) has the potential to advance Intelligent Transportation Systems (ITS). This study explores the current advancements of VLC in ITS applications that may enhance traffic flow, road safety, and vehicular communication performance. The potential, benefits, and current research trends of VLC in ITS applications are discussed first. Then, the state-of-the-art VLC technologies including overall concept, IEEE communication protocols, hybrid VLC systems, and software-defined adaptive MIMO VLC systems, are discussed. We investigated different potential applications of VLC in ITS, such as signalized intersection and ramp metering control, collision warning and avoidance, vehicle localization and detection, and vehicle platooning using vehicle–vehicle (V2V), infrastructure–vehicle (I2V), and vehicle–everything (V2X) communications. Besides, VLC faces several challenges in ITS applications, and these concerns, e.g., environmental issues, communication range issues, standards and infrastructure integration issues, light conditions and integration issues are discussed. Finally, this paper discusses various advanced techniques to enhance VLC performance in ITS applications, such as machine learning-based channel estimation, adaptive beamforming, robust modulation schemes, and hybrid VLC integration. With this review, the authors aim to inform academics, engineers, and policymakers about the status and challenges of VLC in ITS. It is expected that, by applying VLC in ITS, mobility will be safer, more efficient, and sustainable. Full article
(This article belongs to the Special Issue Advancements in Optical Wireless Communication (OWC))
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<p>The concept of visible light communication for V2V and V2I (or I2V) in ITS applications. The VLC system consists of both LoS and NLoS links for sharing information.</p>
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<p>The hybrid VLC–RF systems in ITS applications. The vehicles can communicate with a cellular based station using VLC–RF communications or cellular V2X. When there is a sudden incident, the vehicle can communicate with other vehicles in the next lane for a lane change action via cellular V2X communication.</p>
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<p>Factors influencing the VLC transmission link.</p>
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15 pages, 3046 KiB  
Article
Cluster Partitioning Method for High-PV-Penetration Distribution Network Based on mGA-PSO Algorithm
by Zhu Liu, Guowei Guo, Dehuang Gong, Lingfeng Xuan, Feiwu He, Xinglin Wan and Dongguo Zhou
Energies 2025, 18(5), 1197; https://doi.org/10.3390/en18051197 - 28 Feb 2025
Viewed by 166
Abstract
To tackle the issues of scattered distributed photovoltaic access points and unbalanced cluster partitioning scales, an iterative clustering partitioning method is proposed, a which integrates micro-evolution genetic algorithm and particle swarm optimization (mGA-PSO). In this method, the complementary aspects of active and reactive [...] Read more.
To tackle the issues of scattered distributed photovoltaic access points and unbalanced cluster partitioning scales, an iterative clustering partitioning method is proposed, a which integrates micro-evolution genetic algorithm and particle swarm optimization (mGA-PSO). In this method, the complementary aspects of active and reactive power are quantified as key indicators, and node membership is incorporated to construct a comprehensive metric for the partitioning of a distributed PV cluster. Additionally, to improve the optimal search performance of high-penetration photovoltaic cluster partitioning, an enhanced learning-based modification factor is introduced in the genetic algorithm population selection, and a search and transfer mechanism based on historical population information is incorporated into the particle swarm algorithm. This enhances the particle swarm optimization capability with individual intelligent feedback. Experimental tests on the IEEE 34-node and IEEE 110-node systems demonstrate that the proposed method outperforms GA and PSO approaches in cluster partitioning, improving the convergence speed of the algorithm while avoiding local optima. Full article
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<p>Research framework and methodology overview.</p>
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<p>Methods for generating coding map and adjacency table.</p>
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<p>Initialization process.</p>
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<p>The flowchart of the mGA-PSO algorithm.</p>
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<p>IEEE 34-bus network with distributed PV systems.</p>
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<p>Modularity index and fitness with different weights. (<b>a</b>) Modularity index under the influence of weights. (<b>b</b>) Fitness under the influence of weights.</p>
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<p>Cluster partitioning results. (<b>a</b>) Clustering partitioning results obtained by our indicator. (<b>b</b>) Clustering partitioning results obtained by the indicator from [<a href="#B24-energies-18-01197" class="html-bibr">24</a>].</p>
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<p>IEEE 34-node fitness function variation curve.</p>
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<p>Cluster partitioning results.</p>
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<p>IEEE 110-node fitness function variation curve.</p>
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19 pages, 3481 KiB  
Article
Risk Assessment Method for Power Distribution Systems Based on Spatiotemporal Characteristics of the Typhoon Disaster Chain
by Bin Chen, Nuoling Sun, Hao Chen, Linyao Zhang, Jiawei Wan and Jie Su
Processes 2025, 13(3), 699; https://doi.org/10.3390/pr13030699 - 28 Feb 2025
Viewed by 132
Abstract
In recent years, power outages due to typhoon-induced rainstorms, waterlogging, and other extreme weather events have become increasingly common, and accurately assessing the risk of damage to the distribution system during a disaster is critical to enhancing the resilience of the power system. [...] Read more.
In recent years, power outages due to typhoon-induced rainstorms, waterlogging, and other extreme weather events have become increasingly common, and accurately assessing the risk of damage to the distribution system during a disaster is critical to enhancing the resilience of the power system. Therefore, a risk assessment method for power distribution systems considering the spatiotemporal characteristics of the typhoon disaster chain is proposed. The mechanism of forming the typhoon disaster chain is first analyzed and its spatiotemporal characteristics are modeled. Secondly, the failure probability of the distribution system equipment during the evolution process of the disaster chain is modeled. Then, the non-sequential Monte Carlo state sampling method combined with the distribution system risk assessment index is proposed to establish the disaster risk assessment system of the distribution system. Finally, based on the IEEE 33-bus power system, the proposed distribution system disaster risk assessment method is verified. Simulation solutions show that the proposed assessment method can effectively assess the disaster risk of the distribution system under the influence of the typhoon disaster chain. The simulation results show that at the time step of typhoon landfall, the load shedding reaches 1315.3 kW with a load shedding rate of 35.4%. The total economic loss at the time step is 2,289,200 CNY. These results demonstrate the effectiveness of the proposed method in assessing disaster risks and improving the resilience of power systems during typhoon events. Full article
(This article belongs to the Special Issue Modeling, Optimization, and Control of Distributed Energy Systems)
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<p>Relationships among wind fields.</p>
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<p>Schematic of surface runoff.</p>
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<p>Non-sequential Monte Carlo sampling flow chart.</p>
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<p>The distribution system risk assessment process based on spatiotemporal simulation of typhoon disaster chain.</p>
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<p>(<b>a</b>) The elevation map of the region and the distribution of the IEEE-33 node system; (<b>b</b>) The best path of Typhoon “Doksuri”.</p>
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<p>(<b>a</b>) Wind speed of nodes; (<b>b</b>) Precipitation intensity of nodes.</p>
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<p>(<b>a</b>) Water accumulation depth of nodes; (<b>b</b>) Failure probability of nodes.</p>
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<p>Failure probability of transmission lines.</p>
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<p>Risk indicators of load shedding, voltage overrun, line overload and economic loss at different time steps.</p>
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23 pages, 1378 KiB  
Article
Design and Implementation of an Indoor Localization System Based on RSSI in IEEE 802.11ax
by Roberto Gaona Juárez, Abel García-Barrientos, Jesus Acosta-Elias, Enrique Stevens-Navarro, César G. Galván, Alessio Palavicini and Ernesto Monroy Cruz
Appl. Sci. 2025, 15(5), 2620; https://doi.org/10.3390/app15052620 - 28 Feb 2025
Viewed by 222
Abstract
This article describes the design, implementation, and evaluation of an indoor localization system based on Received Signal Strength Indicator (RSSI) measurements in wireless sensor networks. While the majority of the literature uses the IEEE 802.15 standard for this type of system, all of [...] Read more.
This article describes the design, implementation, and evaluation of an indoor localization system based on Received Signal Strength Indicator (RSSI) measurements in wireless sensor networks. While the majority of the literature uses the IEEE 802.15 standard for this type of system, all of the measurements in this study were performed using a test bench operating under the IEEE 802.11ax standard in the 2.4 GHz band. RSSI is widely used due to its simplicity and availability; however, its accuracy is limited by signal attenuation, electromagnetic interference, and environmental variability. To mitigate these limitations, the present work proposes the implementation of advanced techniques, including weighted averages and positioning algorithms such as Min–Max, Maximum Likelihood, and trilateration, aiming to achieve an accuracy of 2 m in controlled conditions. The design also included a specialized test bench to calculate the coordinates and estimate the location of unknown nodes using anchor node positioning. This approach combines the simplicity of RSSI with optimized algorithms, providing a robust and practical solution for indoor localization. The results validate the system’s effectiveness and highlight its potential for future applications in real-world environments, opening new possibilities for optimizing wireless sensor networks and addressing the current challenges in localization systems. Full article
(This article belongs to the Special Issue Advances in Wireless Sensor Networks and Communication Technology)
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<p>Diagram of the RSSI measurement process using the Physics Toolbox app on the Oppo Reno 11 device.</p>
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<p>Average RSSI as a function of distance.</p>
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<p>Proposed GPS circuit.</p>
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<p>Comparison of RSSI and distance between experimental data and data from Ding and Dong (2020) [<a href="#B1-applsci-15-02620" class="html-bibr">1</a>].</p>
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<p>Relationship between RSSI and distance throughout the hours of the day.</p>
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<p>Dispersion diagram of RSSI and distance.</p>
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<p>Dispersion diagram of RSSI and measurement days.</p>
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<p>Dispersion diagram for relationship between RSSI and measurement hours.</p>
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<p>Path loss model vs. distance.</p>
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<p>Map of the measurement area with anchor nodes and transmitter locations for the trilateration method.</p>
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<p>Map of the measurement area with anchor nodes and transmitter locations for the min–max method.</p>
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<p>Map of the measurement area with anchor nodes and transmitter locations for the Maximum Likelihood method.</p>
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20 pages, 2919 KiB  
Systematic Review
Contribution of Microlearning in Basic Education: A Systematic Review
by Elaine Santana Silva, Woska Pires da Costa, Junio Cesar de Lima and Julio Cesar Ferreira
Educ. Sci. 2025, 15(3), 302; https://doi.org/10.3390/educsci15030302 - 27 Feb 2025
Viewed by 274
Abstract
This systematic review analyzed the role of microlearning in basic education, identifying the most widely used Digital Information and Communication Technologies, relevant learning theories, and the role of social technologies from a Science, Technology, Society, and Environment (STSE) perspective. Following PRISMA 2020, searches [...] Read more.
This systematic review analyzed the role of microlearning in basic education, identifying the most widely used Digital Information and Communication Technologies, relevant learning theories, and the role of social technologies from a Science, Technology, Society, and Environment (STSE) perspective. Following PRISMA 2020, searches were conducted in Web of Science, Scopus, ERIC, and IEEE Xplore databases. Studies on microlearning were selected based on previously defined eligibility criteria. The review process in Rayyan involved deduplication, screening, and full-text analysis. Data were qualitatively analyzed using content analysis, and methodological quality was assessed with CASP and the Downs and Black. The findings highlight that microlearning, integrated with digital tools such as online platforms, mobile apps, and short videos, significantly enhances student motivation, performance, and interaction; content in short modules facilitates knowledge retention and connects concepts to real-life situations. Promising trends include mobile technologies and gamification, which foster active, meaningful learning. Grounded in theories like Self-Determination, Constructionism, and Constructivism, microlearning personalizes teaching and promotes engagement, critical thinking, and accessibility, contributing to inclusive and sustainable education. From a STSE perspective, social technologies enhance autonomy, social interaction, and ethical–environmental awareness. In Brazil, further research on digital platforms and gamified strategies is needed to drive innovative educational practices. Full article
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<p>PRISMA 2020 flow diagram for identifying, screening, and including studies in this review.</p>
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<p>Methodological designs used in the studies included (<span class="html-italic">n</span> = 14).</p>
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<p>Data collection instruments used in the studies included (<span class="html-italic">n</span> = 14).</p>
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<p>Studies on microlearning carried out by continent.</p>
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<p>Analysis diagram of the categories, contexts, and recording units of the articles included.</p>
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<p>The most used DICTs in microlearning studies.</p>
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20 pages, 4180 KiB  
Article
Resilience Assessment Framework for High-Penetration Renewable Energy Power System
by Dongyue Zhou, Xueping Pan, Xiaorong Sun and Funian Hu
Sustainability 2025, 17(5), 2058; https://doi.org/10.3390/su17052058 - 27 Feb 2025
Viewed by 190
Abstract
The random and intermittent nature of renewable energy creates challenges for power systems to cope with sudden disturbances and extreme events. This study establishes a system network model and cascading failure model that consider the power flow relationship between different power sources, and [...] Read more.
The random and intermittent nature of renewable energy creates challenges for power systems to cope with sudden disturbances and extreme events. This study establishes a system network model and cascading failure model that consider the power flow relationship between different power sources, and then the impact of renewable energy on power system resilience is analyzed based on complex network theory. Furthermore, several resilience evaluation indexes are proposed from structural and functional perspectives. Using the system model, a resilience curve suitable for renewable energy power systems is proposed. The electrical degree centrality is used as the index to identify key nodes and simulate random attack and deliberate attack modes. The effectiveness of the evaluation method is verified on the IEEE 118-bus system using the typical time, different access ratios, and distribution characteristics of renewable energy. The results indicate that with high penetration of renewable energy, power systems’ resilience may decline by more than 20% in most cases. Full article
(This article belongs to the Section Energy Sustainability)
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<p>Schematic diagram of the IEEE 30-bus power system with renewable energy.</p>
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<p>Resilience process of a renewable energy power system with (<b>a</b>) component failure rate E<sub>B<span class="html-italic">,t</span></sub><span class="html-italic">,i</span> and (<b>b</b>) load failure rate <span class="html-italic">E</span><sub>B<span class="html-italic">,t</span></sub><span class="html-italic">,o</span>.</p>
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<p>Resilience evaluation framework.</p>
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<p>Cascading failure simulation process.</p>
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<p>Simulation method for extreme events.</p>
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<p>System topology with penetration levels of (<b>a</b>) 0%, (<b>b</b>) 20%, and (<b>c</b>) 50%.</p>
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<p>Typical renewable energy profiles.</p>
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<p>Resilience curves: (<b>a</b>) <span class="html-italic">E<sub>B</sub></span>,<span class="html-italic">i</span> and (<b>b</b>) <span class="html-italic">E<sub>B</sub></span>,<span class="html-italic">o</span>.</p>
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<p>Resilience indexes of the system when the attack time is 11:30 a.m.: (<b>a</b>) largest cluster size, (<b>b</b>) power flow entropy, and (<b>c</b>) loss in power flow.</p>
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<p>Resilience of the system when the attack time is 21:00 p.m.: (<b>a</b>) largest cluster size, (<b>b</b>) power flow entropy, and (<b>c</b>) lack of power.</p>
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<p>System resilience with different penetration levels of renewable energy (the system is with maximum net load and is attacked deliberately): (<b>a</b>) largest cluster size, (<b>b</b>) power flow entropy, and (<b>c</b>) lack of power.</p>
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<p>System resilience with different penetration levels of renewable energy: (<b>a</b>) largest cluster size, (<b>b</b>) power flow entropy, and (<b>c</b>) lack of power.</p>
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<p>Resilience of the system with different distribution characteristics of renewable energy: (<b>a</b>) power flow entropy and (<b>b</b>) lack of power.</p>
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34 pages, 640 KiB  
Article
Brute Force Computations and Reference Solutions
by Mihail Mihaylov Konstantinov, Petko Hristov Petkov and Ekaterina Borisova Madamlieva
Foundations 2025, 5(1), 7; https://doi.org/10.3390/foundations5010007 - 26 Feb 2025
Viewed by 138
Abstract
In this paper, we consider the application of brute force computational techniques (BFCTs) for solving computational problems in mathematical analysis and matrix algebra in a floating-point computing environment. These techniques include, among others, simple matrix computations and the analysis of graphs of functions. [...] Read more.
In this paper, we consider the application of brute force computational techniques (BFCTs) for solving computational problems in mathematical analysis and matrix algebra in a floating-point computing environment. These techniques include, among others, simple matrix computations and the analysis of graphs of functions. Since BFCTs are based on matrix calculations, the program system MATLAB® is suitable for their computer realization. The computations in this paper are completed in double precision floating-point arithmetic, obeying the 2019 IEEE Standard for binary floating-point calculations. One of the aims of this paper is to analyze cases where popular algorithms and software fail to produce correct answers, failing to alert the user. In real-time control applications, this may have catastrophic consequences with heavy material damage and human casualties. It is known, or suspected, that a number of man-made catastrophes such as the Dharhan accident (1991), Ariane 5 launch failure (1996), Boeing 737 Max tragedies (2018, 2019) and others are due to errors in the computer software and hardware. Another application of BFCTs is finding good initial guesses for known computational algorithms. Sometimes, simple and relatively fast BFCTs are useful tools in solving computational problems correctly and in real time. Among particular problems considered are the genuine addition of machine numbers, numerically stable computations, finding minimums of arrays, the minimization of functions, solving finite equations, integration and differentiation, computing condensed and canonical forms of matrices and clarifying the concepts of the least squares method in the light of the conflict remainders vs. errors. Usually, BFCTs are applied under the user’s supervision, which is not possible in the automatic implementation of computational methods. To implement BFCTs automatically is a challenging problem in the area of artificial intelligence and of mathematical artificial intelligence in particular. BFCTs allow to reveal the underlying arithmetic in the performance of computational algorithms. Last but not least, this paper has tutorial value, as computational algorithms and mathematical software are often taught without considering the properties of computational algorithms and machine arithmetic. Full article
(This article belongs to the Section Mathematical Sciences)
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<p>Scaled rounding errors.</p>
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<p>An oscillating function.</p>
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<p>Computed first difference of the function <math display="inline"><semantics> <mrow> <mi>f</mi> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>=</mo> <mi>x</mi> </mrow> </semantics></math>.</p>
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