<?xml version="1.0" encoding="UTF-8"?>
<article article-type="research-article" dtd-version="1.3" xml:lang="ru" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="https://metafora.rcsi.science/xsd_files/journal3.xsd">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">moitvivt</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Моделирование, оптимизация и информационные технологии</journal-title>
        <trans-title-group xml:lang="en">
          <trans-title>Modeling, Optimization and Information Technology</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn pub-type="epub">2310-6018</issn>
      <publisher>
        <publisher-name>Издательство</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.26102/2310-6018/2023.40.1.003</article-id>
      <article-id pub-id-type="custom" custom-type="elpub">1297</article-id>
      <title-group>
        <article-title xml:lang="ru">Методика построения траектории беспилотных летательных аппаратов для автономного сбора визуальных данных о повреждениях линий электропередач в инфракрасном и ультрафиолетовом спектрах</article-title>
        <trans-title-group xml:lang="en">
          <trans-title>The methodology for unmanned aerial vehicle trajectory forming for the autonomous gathering of visual data on electric powerline defects in infrared and ultraviolet spectra</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">0000-0002-9121-894X</contrib-id>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Астапова</surname>
              <given-names>Марина Алексеевна</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Astapova</surname>
              <given-names>Marina Alekseevna</given-names>
            </name>
          </name-alternatives>
          <email>marinaastapova55@gmail.com</email>
          <xref ref-type="aff">aff-1</xref>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">0000-0002-4423-1308</contrib-id>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Лебедев</surname>
              <given-names>Игорь Владимирович</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Lebedev</surname>
              <given-names>Igor Vladimirovich</given-names>
            </name>
          </name-alternatives>
          <email>igorlevedev@gmail.com</email>
          <xref ref-type="aff">aff-2</xref>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">0000-0002-7032-0291</contrib-id>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Уздяев</surname>
              <given-names>Михаил Юрьевич</given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Uzdiaev</surname>
              <given-names>Mikhail Yurievich</given-names>
            </name>
          </name-alternatives>
          <email>uzdyaev.m@iias.spb.su</email>
          <xref ref-type="aff">aff-3</xref>
        </contrib>
      </contrib-group>
      <aff-alternatives id="aff-1">
        <aff xml:lang="ru">Санкт-Петербургский Федеральный исследовательский центр Российской академии наук</aff>
        <aff xml:lang="en">St. Petersburg Federal Research Center of the Russian Academy of Sciences</aff>
      </aff-alternatives>
      <aff-alternatives id="aff-2">
        <aff xml:lang="ru">Санкт-Петербургский Федеральный исследовательский центр Российской академии наук</aff>
        <aff xml:lang="en">St. Petersburg Federal Research Center of the Russian Academy of Sciences</aff>
      </aff-alternatives>
      <aff-alternatives id="aff-3">
        <aff xml:lang="ru">Санкт-Петербургский Федеральный исследовательский центр Российской академии наук</aff>
        <aff xml:lang="en">St. Petersburg Federal Research Center of the Russian Academy of Sciences</aff>
      </aff-alternatives>
      <pub-date pub-type="epub">
        <day>01</day>
        <month>01</month>
        <year>2026</year>
      </pub-date>
      <volume>1</volume>
      <issue>1</issue>
      <elocation-id>10.26102/2310-6018/2023.40.1.003</elocation-id>
      <permissions>
        <copyright-statement>Copyright © Авторы, 2026</copyright-statement>
        <copyright-year>2026</copyright-year>
        <license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/">
          <license-p>This work is licensed under a Creative Commons Attribution 4.0 International License</license-p>
        </license>
      </permissions>
      <self-uri xlink:href="https://moitvivt.ru/ru/journal/article?id=1297"/>
      <abstract xml:lang="ru">
        <p>Нагрев элементов линий электропередач (ЛЭП) и коронные разряды, возникающие на токопроводящих элементах ЛЭП, являются серьезными проблемами, которые могут привести к отказам в энергетической системе. Выявление данных повреждений требует специализированного оборудования, позволяющего получать изображения в инфракрасном (ИК) спектре для обнаружения нагрева и в ультрафиолетовом (УФ) спектре для обнаружения коронного разряда. Использование автономных беспилотных летательных аппаратов (БпЛА), оборудованных специализированными средствами съемки, позволяет автоматизировать процесс инспекции обозначенных повреждений. При этом траектория автономного движения БпЛА должна строиться с учетом пространственно-геометрических особенностей инспектируемых ЛЭП, а также требований к выборке изображений, получаемой в ходе инспекции повреждений ЛЭП. Однако вопросы построения траекторий движения с учетом обозначенных требований остаются во многом не проработаны. В рамках данного исследования предлагается новая методика построения траекторий движения БпЛА, отличающаяся формированием параметров траектории с учетом конструкционных ЛЭП (пространственное расположение и геометрические характеристики башен ЛЭП, и ключевых элементов (КЭ) ЛЭП), и требований к собираемым данным (наличие повреждений в кадре, репрезентативность объектов, унифицированность представленных объектов). Для проверки методики в среде трехмерного моделирования Blender была выполнена симуляция автономной инспекции нагрева проводов и коронного разряда у трех видов ЛЭП посредством автономного БпЛА. В результате была собрана выборка изображений в ИК, и УФ спектрах, состоящая из 1300 изображений, на которых представлено 1376 уникальных ракурсов 17 симулированных повреждений, унифицированных для каждого типа ЛЭП, что свидетельствует о перспективе данной методики для построения траекторий автономного полета БпЛА с целью сбора репрезентативных выборок данных о повреждениях ЛЭП в УФ и ИК спектрах.</p>
      </abstract>
      <trans-abstract xml:lang="en">
        <p>Powerline element heat and corona discharge occurring in current conducting elements are significant problems that may cause serious faults in energetic systems. These defects require special equipment that makes it possible to obtain images in infrared (IR) and ultraviolet (UV) spectra for heat and corona discharge detection, respectively. The use of autonomous unmanned aerial vehicles (UAV) equipped with the appropriate cameras provide automation of such defect detection. Concurrently, the trajectory of the autonomous UAV should be formed according to the spatio-geometric features of the inspected power lines and the requirements for the image sample obtained during the inspection of the damaged powerline. However, the issues related to forming UAV trajectory consistent with the specified requirements have not been properly explored. As part of this research, a new method for UAV trajectory forming is presented. The method is characterized by forming the trajectory according to the spatio-geometric features of the inspected powerlines with its key components and the requirements for the collected data (the presence of damage in the image, object representativeness, unification of the represented objects). The method was tested in the Blender 3D modeling environment by simulation of the autonomous wire heating and corona discharge inspection in three powerline types. As a result, a sample of IR and UV spectra images was collected. The sample consists of 1300 images, which represents 1376 unique angles of 17 cases of simulated damage, which indicates the viability of this technique for constructing UAV autonomous flight trajectories in order to collect representative sample data on powerline damage in UV and IR spectra.</p>
      </trans-abstract>
      <kwd-group xml:lang="ru">
        <kwd>автономные беспилотные летательные аппараты</kwd>
        <kwd>построение траекторий</kwd>
        <kwd>автоматический мониторинг</kwd>
        <kwd>алгоритмы аэросъемки</kwd>
        <kwd>сбор данных</kwd>
      </kwd-group>
      <kwd-group xml:lang="en">
        <kwd>autonomous UAVs</kwd>
        <kwd>trajectory construction</kwd>
        <kwd>automatic monitoring</kwd>
        <kwd>aerial survey algorithms</kwd>
        <kwd>data collection</kwd>
      </kwd-group>
      <funding-group>
        <funding-statement xml:lang="ru">Работа выполнена при финансовой поддержке РФФИ в рамках научного проекта №20-08-01056 А.</funding-statement>
        <funding-statement xml:lang="en">The reported research was carried out with the financial support of the Russian Foundation for Basic Research as part of scientific project No. 20-08-01056 A.</funding-statement>
      </funding-group>
    </article-meta>
  </front>
  <back>
    <ref-list>
      <title>References</title>
      <ref id="cit1">
        <label>1</label>
        <mixed-citation xml:lang="ru">Gazebo. Доступно по: https://gazebosim.org/home (дата обращения: 16.11.2022).</mixed-citation>
      </ref>
      <ref id="cit2">
        <label>2</label>
        <mixed-citation xml:lang="ru">Blender Studio. Доступно по: https://www.blender.org/ (дата обращения: 16.11.2022).</mixed-citation>
      </ref>
      <ref id="cit3">
        <label>3</label>
        <mixed-citation xml:lang="ru">Астапова М.А., Лебедев И.В. Обзор подходов к детектированию дефектов элементов ЛЭП на изображениях в инфракрасном, ультрафиолетовом и видимом спектрах. Моделирование, оптимизация и информационные технологии. 2020;8(4):38–39.</mixed-citation>
      </ref>
      <ref id="cit4">
        <label>4</label>
        <mixed-citation xml:lang="ru">Liu W., Wang Z., Liu X., Zeng N., Liu Y., Alsaadi F.E. A survey of deep neural network architectures and their applications. Neurocomputing. 2017;234:11–26.</mixed-citation>
      </ref>
      <ref id="cit5">
        <label>5</label>
        <mixed-citation xml:lang="ru">Liu L., Ouyang W., Wang X., Fieguth P., Chen J., Liu X., Pietikäinen M. Deep learning for generic object detection: A survey. International journal of computer vision. 2020;128(2):261–318.</mixed-citation>
      </ref>
      <ref id="cit6">
        <label>6</label>
        <mixed-citation xml:lang="ru">Zaidi S.S., Ansari M.S., Aslam A., Kanwal N., Asghar M., Lee B. A survey of modern deep learning based object detection models. Digital Signal Processing. 2022;8:103514.</mixed-citation>
      </ref>
      <ref id="cit7">
        <label>7</label>
        <mixed-citation xml:lang="ru">Hao S., Zhou Y., Guo Y. A brief survey on semantic segmentation with deep learning. Neurocomputing. 2020;406:302–21.</mixed-citation>
      </ref>
      <ref id="cit8">
        <label>8</label>
        <mixed-citation xml:lang="ru">Hafiz A.M., Bhat G.M. A survey on instance segmentation: state of the art. International journal of multimedia information retrieval. 2020;9(3):171–189.</mixed-citation>
      </ref>
      <ref id="cit9">
        <label>9</label>
        <mixed-citation xml:lang="ru">Kirillov A., He K., Girshick R., Rother C., Dollár P. Panoptic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2019:9404–9413.</mixed-citation>
      </ref>
      <ref id="cit10">
        <label>10</label>
        <mixed-citation xml:lang="ru">Bengio Y., Lecun Y., Hinton G. Deep learning for AI. Communications of the ACM. 2021;64(7):58–65.</mixed-citation>
      </ref>
      <ref id="cit11">
        <label>11</label>
        <mixed-citation xml:lang="ru">Gondal M.W., Wuthrich M., Miladinovic D., Locatello F., Breidt M., Volchkov V., Akpo J., Bachem O., Schölkopf B., Bauer S. On the transfer of inductive bias from simulation to the real world: a new disentanglement dataset. Advances in Neural Information Processing Systems. 2019;32.</mixed-citation>
      </ref>
      <ref id="cit12">
        <label>12</label>
        <mixed-citation xml:lang="ru">Reed S.E., Zhang Y., Zhang Y., Lee H. Deep visual analogy-making. Advances in neural information processing systems. 2015;28.</mixed-citation>
      </ref>
      <ref id="cit13">
        <label>13</label>
        <mixed-citation xml:lang="ru">LeCun Y., Huang F.J., Bottou L. Learning methods for generic object recognition with invariance to pose and lighting. In Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR). 2004;2:II–104.</mixed-citation>
      </ref>
      <ref id="cit14">
        <label>14</label>
        <mixed-citation xml:lang="ru">Попов Н.И., Емельянова О.В. Динамические особенности мониторинга воздушных линий электропередачи с помощью квадрокоптера. Современные проблемы науки и образования. 2014;2:105.</mixed-citation>
      </ref>
      <ref id="cit15">
        <label>15</label>
        <mixed-citation xml:lang="ru">Liu Y., Huo H., Fang J., Mai J., Zhang S. UAV Transmission line inspection object recognition based on Mask R-CNN. In Journal of Physics: Conference Series;1345(6):062043.</mixed-citation>
      </ref>
      <ref id="cit16">
        <label>16</label>
        <mixed-citation xml:lang="ru">He K., Gkioxari G., Dollar P., Girshick R. Mask R-CNN. Proceedings of the IEEE international conference on computer vision. 2017;2961–2969.</mixed-citation>
      </ref>
      <ref id="cit17">
        <label>17</label>
        <mixed-citation xml:lang="ru">Liu X., Lin Y., Jiang H., Miao X., Chen J. Slippage fault diagnosis of dampers for transmission lines based on faster R-CNN and distance constraint. Electric Power Systems Research. 2021;199:107449.</mixed-citation>
      </ref>
      <ref id="cit18">
        <label>18</label>
        <mixed-citation xml:lang="ru">Ren S., He K., Girshick R., Sun J. Faster r-cnn: Towards real-time object detection with region proposal networks. Advances in neural information processing systems. 2015;28.</mixed-citation>
      </ref>
      <ref id="cit19">
        <label>19</label>
        <mixed-citation xml:lang="ru">Lebedev I., Izhboldina V. Method for Inspecting High-voltage Power Lines Using UAV Based on the RRT Algorithm. In Electromechanics and Robotics. 2022:179–190.</mixed-citation>
      </ref>
      <ref id="cit20">
        <label>20</label>
        <mixed-citation xml:lang="ru">Chen L., Lin L., Tian M., Bian X., Wang L., Guan Z. The ultraviolet detection of corona discharge in power transmission lines. Energy Power Eng. 2013;5(04):1298.</mixed-citation>
      </ref>
      <ref id="cit21">
        <label>21</label>
        <mixed-citation xml:lang="ru">Moore A.J., Schubert M., Rymer N. Technologies and operations for high voltage corona detection with UAVs. In 2018 IEEE Power &amp; Energy Society General Meeting (PESGM). 2018;5:1–5.</mixed-citation>
      </ref>
      <ref id="cit22">
        <label>22</label>
        <mixed-citation xml:lang="ru">Nguyen P., Dudkin S., Kong C. Automatic diagnostic of transmission lines based on ultraviolet inspection. In E3S Web of Conferences. 2019;140:07008.</mixed-citation>
      </ref>
      <ref id="cit23">
        <label>23</label>
        <mixed-citation xml:lang="ru">Davari N., Akbarizadeh G., Mashhour E. Intelligent diagnosis of incipient fault in power distribution lines based on corona detection in UV-visible videos. IEEE Transactions on Power Delivery. 2020;36(6):3640–8.</mixed-citation>
      </ref>
      <ref id="cit24">
        <label>24</label>
        <mixed-citation xml:lang="ru">Zhao Z., Xu G., Qi Y. Representation of binary feature pooling for detection of insulator strings in infrared images. IEEE Transactions on Dielectrics and Electrical Insulation. 2016;23(5):2858–2866.</mixed-citation>
      </ref>
      <ref id="cit25">
        <label>25</label>
        <mixed-citation xml:lang="ru">Ullah I., Khan R.U., Yang F., Wuttisittikulkij L. Deep learning image-based defect detection in high voltage electrical equipment. Energies. 2020;13(2):392.</mixed-citation>
      </ref>
      <ref id="cit26">
        <label>26</label>
        <mixed-citation xml:lang="ru">Nie J., Luo T., Li H. Automatic hotspots detection based on UAV infrared images for large‐scale PV plant. Electronics Letters. 2020;56(19):993–995.</mixed-citation>
      </ref>
      <ref id="cit27">
        <label>27</label>
        <mixed-citation xml:lang="ru">Tao X., Zhang D., Wang Z., Liu X., Zhang H., Xu D. Detection of Power Line Insulator Defects Using Aerial Images Analyzed With Convolutional Neural Networks. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2020;50(4):1486–1498.</mixed-citation>
      </ref>
      <ref id="cit28">
        <label>28</label>
        <mixed-citation xml:lang="ru">Ömer E.Y., Ömer N.G. Powerline Image Dataset (Infrared-IR and Visible Light-VL). 2019. Доступно по: https://data.mendeley.com/datasets/n6wrv4ry6v/8 (дата обращения: 16.12.2021).</mixed-citation>
      </ref>
      <ref id="cit29">
        <label>29</label>
        <mixed-citation xml:lang="ru">Bian J., Hui X., Zhao X., Tan M. A monocular vision-based perception approach for unmanned aerial vehicle close proximity transmission tower inspection. International Journal of Advanced Robotic Systems. 2019;16(1):1729881418820227.</mixed-citation>
      </ref>
      <ref id="cit30">
        <label>30</label>
        <mixed-citation xml:lang="ru">Wu C., Ma X., Kong X., Zhu H. Research on insulator defect detection algorithm of transmission line based on CenterNet. Plos one. 2021;16(7):e0255135.</mixed-citation>
      </ref>
      <ref id="cit31">
        <label>31</label>
        <mixed-citation xml:lang="ru">Vieira-e-Silva A.L., de Castro Felix H., de Menezes Chaves T., Simões F.P., Teichrieb V., dos Santos M.M., da Cunha Santiago H., Sgotti V.A., Neto H.B. STN PLAD: A Dataset for Multi-Size Power Line Assets Detection in High-Resolution UAV Images. In 2021 34th SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI). 2021:215-222.</mixed-citation>
      </ref>
      <ref id="cit32">
        <label>32</label>
        <mixed-citation xml:lang="ru">Abdelfattah R., Wang X., Wang S. Ttpla: An aerial-image dataset for detection and segmentation of transmission towers and power lines. In Proceedings of the Asian Conference on Computer Vision. 2020.</mixed-citation>
      </ref>
      <ref id="cit33">
        <label>33</label>
        <mixed-citation xml:lang="ru">Монтаж и эксплуатация воздушных линий электропередачи. Доступно по: https://elektro-montagnik.ru/?address=lectures/part2/&amp;page=page1 (дата обращения: 16.11.2022).</mixed-citation>
      </ref>
      <ref id="cit34">
        <label>34</label>
        <mixed-citation xml:lang="ru">Chermoshencev S.F., Gaynutdinov R.R. Modeling the external electromagnetic influences on the complex electronic equipment. In2 015 XVIII International Conference on Soft Computing and Measurements (SCM). 2015:90–92.</mixed-citation>
      </ref>
      <ref id="cit35">
        <label>35</label>
        <mixed-citation xml:lang="ru">Huang L., Xu D., Zhai D. Research and design of space-sky-ground integrated transmission line inspection platform based on artificial intelligence. In 2018 2nd IEEE Conference on Energy Internet and Energy System Integration (EI2). 2018:1–4.</mixed-citation>
      </ref>
      <ref id="cit36">
        <label>36</label>
        <mixed-citation xml:lang="ru">Шабанова А.Р., Толстой М.И., Лебедев И.В. Способ построения безопасных траекторий движения беспилотного летательного аппарата при мониторинге линий электропередач в условиях влияния электромагнитных полей. Проблемы региональной энергетики. 2019;3(44).</mixed-citation>
      </ref>
      <ref id="cit37">
        <label>37</label>
        <mixed-citation xml:lang="ru">Riba J.R., Abomailek C., CasalsTorrens P., Capelli F. Simplification and cost reduction of visual corona tests. IET Generation, Transmission &amp; Distribution. 2018;12(4):834–41.</mixed-citation>
      </ref>
      <ref id="cit38">
        <label>38</label>
        <mixed-citation xml:lang="ru">Gaussorgues G., Chomet S. Infrared thermography. Springer Science &amp; Business Media. 1993;5.</mixed-citation>
      </ref>
      <ref id="cit39">
        <label>39</label>
        <mixed-citation xml:lang="ru">Junior3d.ru – Сайт о 3D. Доступно по: https://junior3d.ru/ (дата обращения: 16.11.2022).</mixed-citation>
      </ref>
      <ref id="cit40">
        <label>40</label>
        <mixed-citation xml:lang="ru">Free3D. Доступно по: https://free3d.com/ (дата обращения: 16.11.2022).</mixed-citation>
      </ref>
      <ref id="cit41">
        <label>41</label>
        <mixed-citation xml:lang="ru">Image Polygonal Annotation with Python. Доступно по: https://zenodo.org/record/5711226#.Yw14ShxBy5c. DOI: 10.5281/zenodo.5711225 (дата обращения 21.11.22).</mixed-citation>
      </ref>
    </ref-list>
    <fn-group>
      <fn fn-type="conflict">
        <p>The authors declare that there are no conflicts of interest present.</p>
      </fn>
    </fn-group>
  </back>
</article>