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  <front>
    <journal-meta>
      <journal-id journal-id-type="issn">2411-3336</journal-id>
      <journal-id journal-id-type="eissn">2541-9404</journal-id>
      <journal-title-group>
        <journal-title xml:lang="ru">Записки Горного института</journal-title>
        <journal-title xml:lang="en">Journal of Mining Institute</journal-title>
      </journal-title-group>
      <publisher>
        <publisher-name xml:lang="ru">Санкт-Петербургский горный университет императрицы Екатерины ΙΙ</publisher-name>
        <publisher-name xml:lang="en">Empress Catherine II Saint Petersburg Mining University</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id custom-type="edn" pub-id-type="custom">QIWCEK</article-id>
      <article-id custom-type="pmi" pub-id-type="custom">pmi-16663</article-id>
      <article-id pub-id-type="uri">https://pmi.spmi.ru/pmi/article/view/16663</article-id>
      <article-categories>
        <subj-group subj-group-type="section-heading" xml:lang="ru">
          <subject>Геотехнология и инженерная геология</subject>
        </subj-group>
        <subj-group subj-group-type="section-heading" xml:lang="en">
          <subject>Geotechnical Engineering and Engineering Geology</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title xml:lang="en">Predicting gas hydrate formation temperature using a hybrid artificial intelligence-empirical approach</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Прогнозирование температуры образования газовых гидратов с использованием гибридного подхода на основе искусственного интеллекта и эмпирических данных</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Riazi</surname>
            <given-names>Mohsen </given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Риази</surname>
              <given-names>М. </given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Riazi</surname>
              <given-names>Mohsen </given-names>
            </name>
          </name-alternatives>
          <email>pmi@spmi.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <aff-alternatives id="aff1">
          <aff>
            <institution xml:lang="ru">Университет им. Шахида Бахонара в Кермане (Керман, Иран)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Shahid Bahonar University of Kerman (Kerman, Iran)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Mehrjoo</surname>
            <given-names>Hossein </given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Мехраджу</surname>
              <given-names>Х. </given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Mehrjoo</surname>
              <given-names>Hossein </given-names>
            </name>
          </name-alternatives>
          <email>pmi@spmi.ru</email>
          <xref ref-type="aff" rid="aff2"/>
        </contrib>
        <aff-alternatives id="aff2">
          <aff>
            <institution xml:lang="ru">Университет им. Шахида Бахонара в Кермане (Керман, Иран)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Shahid Bahonar University of Kerman (Kerman, Iran)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Dabiri</surname>
            <given-names>Mohammad-Saber </given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Дабири</surname>
              <given-names>М.-С. </given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Dabiri</surname>
              <given-names>Mohammad-Saber </given-names>
            </name>
          </name-alternatives>
          <email>pmi@spmi.ru</email>
          <xref ref-type="aff" rid="aff3"/>
        </contrib>
        <aff-alternatives id="aff3">
          <aff>
            <institution xml:lang="ru">Университет им. Шахида Бахонара в Кермане (Керман, Иран)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Shahid Bahonar University of Kerman (Kerman, Iran)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author">
          <name name-style="eastern">
            <surname>Ismailova</surname>
            <given-names>Jamilyam </given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Исмаилова</surname>
              <given-names>Дж. </given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Ismailova</surname>
              <given-names>Jamilyam </given-names>
            </name>
          </name-alternatives>
          <email>pmi@spmi.ru</email>
          <xref ref-type="aff" rid="aff4"/>
        </contrib>
        <aff-alternatives id="aff4">
          <aff>
            <institution xml:lang="ru">Казахский национальный исследовательский технический университет им. К.И.Сатпаева (Алматы, Казахстан)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Satbayev University (Almaty, Kazakhstan)</institution>
          </aff>
        </aff-alternatives>
        <contrib contrib-type="author" corresp="yes">
          <name name-style="eastern">
            <surname>Riazi</surname>
            <given-names>Masoud </given-names>
          </name>
          <name-alternatives>
            <name name-style="eastern" xml:lang="ru">
              <surname>Риази</surname>
              <given-names>М. </given-names>
            </name>
            <name name-style="western" xml:lang="en">
              <surname>Riazi</surname>
              <given-names>Masoud </given-names>
            </name>
          </name-alternatives>
          <email>masoud.riazi@nu.edu.kz</email>
          <xref ref-type="aff" rid="aff5"/>
        </contrib>
        <aff-alternatives id="aff5">
          <aff>
            <institution xml:lang="ru">Назарбаев Университет (Астана, Казахстан)</institution>
          </aff>
          <aff>
            <institution xml:lang="en">Nazarbayev University (Astana, Kazakhstan)</institution>
          </aff>
        </aff-alternatives>
      </contrib-group>
      <pub-date pub-type="epub" iso-8601-date="2026-08-28">
        <day>28</day>
        <month>08</month>
        <year>2026</year>
      </pub-date>
      <pub-date date-type="collection">
        <year>2026</year>
      </pub-date>
      <volume>280</volume>
      <fpage>145</fpage>
      <lpage>162</lpage>
      <history>
        <date date-type="received" iso-8601-date="2025-02-09">
          <day>09</day>
          <month>02</month>
          <year>2025</year>
        </date>
        <date date-type="accepted" iso-8601-date="2026-06-25">
          <day>25</day>
          <month>06</month>
          <year>2026</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2026-08-31">
          <day>31</day>
          <month>08</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement xml:lang="ru">© 2026 М.  Риази, Х.  Мехраджу, М.-С.  Дабири, Дж.  Исмаилова, М.  Риази</copyright-statement>
        <copyright-statement xml:lang="en">© 2026 Mohsen  Riazi, Hossein  Mehrjoo, Mohammad-Saber  Dabiri, Jamilyam  Ismailova, Masoud  Riazi</copyright-statement>
        <copyright-year>2026</copyright-year>
        <copyright-holder xml:lang="ru">М.  Риази, Х.  Мехраджу, М.-С.  Дабири, Дж.  Исмаилова, М.  Риази</copyright-holder>
        <copyright-holder xml:lang="en">Mohsen  Riazi, Hossein  Mehrjoo, Mohammad-Saber  Dabiri, Jamilyam  Ismailova, Masoud  Riazi</copyright-holder>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="ru">
          <license-p>Эта статья доступна по лицензии Creative Commons Attribution 4.0 International (CC BY 4.0)</license-p>
        </license>
        <license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0" xml:lang="en">
          <license-p>This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0)</license-p>
        </license>
      </permissions>
      <self-uri xlink:type="simple" xlink:href="https://pmi.spmi.ru/pmi/article/view/16663">https://pmi.spmi.ru/pmi/article/view/16663</self-uri>
      <abstract xml:lang="ru">
        <p>Точное прогнозирование температуры образования газовых гидратов необходимо для обеспечения бесперебойной подачи при добыче природного газа и его подводной транспортировке. В данном исследовании использовали 459 экспериментальных точек данных, собранных из литературных источников и охватывающих широкий диапазон давлений – 330-68600 кПа, а также диапазон удельной плотности газа – 0,552-1,03. Эти данные послужили основой для разработки надежных инструментов прогнозирования с использованием всего двух практических входных переменных – давления и удельной плотности газа. Были реализованы два взаимо-дополняющих подхода к моделированию. Во-первых, проведен систематический сравнительный анализ нескольких передовых методов машинного обучения, включая многослойный перцептрон (MLP), обученный с применением алгоритмов Левенберга – Марквардта (LM), байесовской регуляризации (BR) и алгоритма масштабируемых сопряженных градиентов (SCG); сеть радиально базисных функций (RBF); CatBoost; XGBoost; метод опорных векторов с использованием метода наименьших квадратов (LSSVM). Во-вторых, сформулирована оптимизированная эмпирическая корреляция, коэффициенты которой определены с помощью алгоритма нелинейной оптимизации обобщенного приведенного градиента (GRG) для минимизации общей погрешности прогнозирования на всем экспериментальном наборе данных. Среди моделей машинного обучения CatBoost продемонстрировал лучшую прогностическую производительность, достигнув значения AAPRE 0,094 % и коэффициента R2 0,996 на тестовом наборе данных. Разработанная корреляция на основе GRG также показала хорошее соответствие экспериментальным данным, одновременно представляя собой прозрачную и вычислительно эффективную альтернативу, подходящую для быстрых инженерных расчетов. Анализ чувствительности и значения рычага подтвердили надежность, статистическую достоверность и широкую применимость предложенных моделей в исследуемой области.</p>
      </abstract>
      <abstract xml:lang="en">
        <p>Accurate prediction of gas hydrate formation temperature is essential for ensuring flow assurance during natural gas production and subsea transportation. In this study, 459 experimental data points collected from the literature, covering a wide pressure range of 330-68,600 kPa and gas specific gravity range of 0.552-1.03, were utilized to develop reliable predictive tools using only two practical input variables: pressure and gas specific gravity. Two complementary modeling approaches were implemented. First, a systematic comparative analysis of several advanced machine learning technique, including Multilayer Perceptron (MLP) trained with Levenberg – Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG) algorithms; Radial Basis Function (RBF); CatBoost; XGBoost; and Least-Squares Support Vector Machine (LSSVM), was conducted. Second, an optimized empirical correlation was formulated, with its coefficients determined using the Generalized Reduced Gradient (GRG) nonlinear optimization algorithm to minimize overall prediction error across the entire experimental dataset. Among the machine learning models, CatBoost demonstrated superior predictive performance, achieving an AAPRE of 0.094 % and an R2 value of 0.996 on the testing dataset. The developed GRG-based correlation also exhibited strong agreement with experimental data while providing a transparent and computationally efficient alternative suitable for rapid engineering calculations. Sensitivity and leverage analyses confirmed the robustness, statistical reliability, and broad applicability of the proposed models within the investigate domain.</p>
      </abstract>
      <kwd-group xml:lang="ru">
        <title>Ключевые слова</title>
        <kwd>температура образования газовых гидратов</kwd>
        <kwd>метод опорных векторов с использованием метода наименьших квадратов</kwd>
        <kwd>машинное обучение</kwd>
        <kwd>многослойный перцептрон</kwd>
        <kwd>сеть радиально базисных функций</kwd>
        <kwd>обобщенный приведенный градиент</kwd>
      </kwd-group>
      <kwd-group xml:lang="en">
        <title>Keywords</title>
        <kwd>gas hydrate temperature</kwd>
        <kwd>least-squares support vector machine</kwd>
        <kwd>machine learning</kwd>
        <kwd>multilayer perceptron</kwd>
        <kwd>radial basis function</kwd>
        <kwd>generalized reduced gradient</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body/>
  <back>
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