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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">sat</journal-id><journal-title-group><journal-title xml:lang="ru">НАУКА и ТЕХНИКА</journal-title><trans-title-group xml:lang="en"><trans-title>Science &amp; Technique</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2227-1031</issn><issn pub-type="epub">2414-0392</issn><publisher><publisher-name>Belarusian National Technical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21122/2227-1031-2025-24-4-327-338</article-id><article-id custom-type="elpub" pub-id-type="custom">sat-2883</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ЭНЕРГЕТИКА</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>POWER ENGINEERING</subject></subj-group></article-categories><title-group><article-title>Многоуровневая стратегия размещения измерительных устройств в инженерных системах с распределенной нагрузкой на основе иерархического и кластерного анализа</article-title><trans-title-group xml:lang="en"><trans-title>Multi-Level Strategy for Placement of Measuring Devices in Engineering Systems  with Distributed Loads Based on Hierarchical and Cluster Analysis</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Капанский</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Kapanski</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Кандидат технических наук, доцент</p><p>Адрес для переписки:Капанский Алексей Александрович -Гомельский государственный технический университет имени П. О. Сухогопросп. Октября, 48,246029, г. Гомель, Республика БеларусьТел.: +375 23 220-48-83</p><p>kapanski@mail.ru</p></bio><bio xml:lang="en"><p>Address for correspondence:Kapanski Aliaksey A. -Gomel State Technical University named after P. O. Sukhoi48, Oktyabrya Аve.,246029, Gomel, Republic of Belarus,</p><p>Tel.: +375 23 220-48-83</p><p>kapanski@mail.ru</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Грунтович</surname><given-names>Н. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Hruntovich</surname><given-names>N. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Доктор технических наук, профессор</p><p>г. Гомель</p></bio><bio xml:lang="en"><p>Gomel</p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Гомельский государственный технический университет имени П. О. Сухого</institution><country>Беларусь</country></aff><aff xml:lang="en"><institution>Gomel State Technical University named after P. O. Sukhoi</institution><country>Belarus</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>01</day><month>09</month><year>2025</year></pub-date><volume>24</volume><issue>4</issue><fpage>327</fpage><lpage>338</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Капанский А.А., Грунтович Н.В., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Капанский А.А., Грунтович Н.В.</copyright-holder><copyright-holder xml:lang="en">Kapanski A.A., Hruntovich N.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://sat.bntu.by/jour/article/view/2883">https://sat.bntu.by/jour/article/view/2883</self-uri><abstract><p>Построение цифровой модели «умного города» в условиях стремительного развития технической инфраструктуры требует эффективных методов мониторинга и управления инженерными системами. Одной из ключевых задач является оптимизация размещения измерительных устройств в таких системах, как водо- и энергоснабжение, включая газ, электричество и теплоту. В условиях ограниченных финансовых ресурсов и необходимости обеспечения высокой точности мониторинга важно учитывать не только географическое распределение потребителей, но и интенсивность их нагрузки. Это особенно актуально для управления распределенными техническими системами, где необходимо минимизировать затраты на оборудование, обеспечивая при этом полный охват сети и своевременное выявление аномалий. Целью данного исследования является разработка методологии оптимального размещения измерительных устройств в инженерных системах, учитывающей как пространственное положение потребителей, так и их загрузку. В работе используется многоуровневая стратегия анализа с применением метода Уорда для иерархической кластеризации и алгоритма k-средних. На основе предложенной методологии на примере системы водоснабжения Гомеля выделены четыре территориальных кластера, на основе которых пропорционально вкладу потребления распределены 20 датчиков давления. В статье показано, как с помощью многопараметрической кластеризации можно определить оптимальные центры размещения измерительных устройств, которые ориентируются на более мощных потребителей, при этом учитывая географическое распределение объектов в целом. Разработанный подход позволяет эффективно распределять измерительные устройства с учетом реальной загрузки объектов в системе и их географического положения, что обеспечивает наилучший охват территории в условиях ограниченного количества оборудования. Приведенный в статье подход может быть адаптирован для различных технических систем, обеспечивая универсальность и гибкость применения.</p></abstract><trans-abstract xml:lang="en"><p>Building a digital model of a “smart city” in the context of rapid development of technical infrastructure requires effective methods for monitoring and managing engineering systems. One of the key tasks is to optimize the placement of measuring devices in systems such as water and energy supply, including gas, electricity and heat. In conditions of limited financial resources and the need to ensure high monitoring accuracy, it is important to take into account not only the geographical distribution of consumers, but also the intensity of their load. This is especially important for managing distributed technical systems, where it is necessary to minimize equipment costs, while ensuring full network coverage and timely detection of anomalies. The purpose of this study is to develop a methodology for the optimal placement of measuring devices in engineering systems that takes into account both the spatial location of consumers and their load. The paper uses a multilevel analysis strategy using Ward’s method for hierarchical clustering and the k-means algorithm. Based on the proposed methodology, four territorial clusters were identified using the example of the Gomel water supply system, on the basis of which 20 pressure sensors were distributed proportionally to the contribution of consumption. The article shows how multiparameter clustering can be used to determine optimal centers for placing measuring devices that are focused on more powerful consumers, while taking into account the geographic distribution of objects as a whole. The developed approach allows for the efficient distribution of measuring devices taking into account the actual load of objects in the system and their geographic location, which ensures the best coverage of the territory under conditions of a limited amount of equipment. The approach presented in the article can be adapted for various technical systems, ensuring universality and flexibility of application.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>многопараметрическая кластеризация</kwd><kwd>оптимизация размещения</kwd><kwd>измерительные устройства</kwd><kwd>распределенная нагрузка</kwd><kwd>географическое распределение</kwd><kwd>центроиды</kwd><kwd>алгоритм k-средних</kwd><kwd>инженерные системы</kwd><kwd>мониторинг</kwd><kwd>цифровая модель</kwd></kwd-group><kwd-group xml:lang="en"><kwd>multi-parameter clustering</kwd><kwd>placement optimization</kwd><kwd>measuring devices</kwd><kwd>distributed load</kwd><kwd>geographic distribution</kwd><kwd>centroids</kwd><kwd>k-means algorithm</kwd><kwd>engineering systems</kwd><kwd>monitoring</kwd><kwd>digital model</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Настоящее исследование выполнено в рамках научно-исследовательской работы «Совершенство-вание методов непараметрической кластеризации для оптимизации управления и повышения энер-гоэффективности городского водоснабжения», финансируемой за счет средств республиканского бюджета Республики Беларусь в соответствии с грантом Министерства образования на 2025 год.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Gautam, D. 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