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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">zldm</journal-id><journal-title-group><journal-title xml:lang="ru">Заводская лаборатория. Диагностика материалов</journal-title><trans-title-group xml:lang="en"><trans-title>Industrial laboratory. Diagnostics of materials</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1028-6861</issn><issn pub-type="epub">2588-0187</issn><publisher><publisher-name>ООО «Издательство «ТЕСТ-ЗЛ»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26896/1028-6861-2026-92-7-77-88</article-id><article-id custom-type="elpub" pub-id-type="custom">zldm-2890</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>МАТЕМАТИЧЕСКИЕ МЕТОДЫ ИССЛЕДОВАНИЯ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MATHEMATICAL METHODS OF INVESTIGATION</subject></subj-group></article-categories><title-group><article-title>Алгоритм построения мультимодальной идентификационной модели с циклическим обучением для процессов с переменной динамикой</article-title><trans-title-group xml:lang="en"><trans-title>An algorithm for constructing a multimodal identification model with cyclic learning for dynamic process with changing dynamics</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>Кушнарев</surname><given-names>В. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Kushnarev</surname><given-names>V. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Владислав Николаевич Кушнарев</p><p>117997, Москва, ул. Профсоюзная, д. 65</p></bio><bio xml:lang="en"><p>Vladislav N. Kushnarev</p><p>65, Profsoyuznaya ul., Moscow, 117997</p></bio><email xlink:type="simple">grand_yarl@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт проблем управления (ИПУ РАН)</institution><country>Россия</country></aff><aff xml:lang="en"><institution>V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>26</day><month>07</month><year>2026</year></pub-date><volume>92</volume><issue>7</issue><fpage>77</fpage><lpage>88</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Кушнарев В.Н., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Кушнарев В.Н.</copyright-holder><copyright-holder xml:lang="en">Kushnarev V.N.</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://www.zldm.ru/jour/article/view/2890">https://www.zldm.ru/jour/article/view/2890</self-uri><abstract><p>Предложен новый подход к идентификации технологических процессов с переменной динамикой, который заключается в статистическом анализе взаимозависимостей между входными и выходными параметрами процесса. Разработан метод для выявления режимов процесса, основанный на вероятностном латентном анализе при помощи EM-алгоритма. Процесс с переменной динамикой описывается при помощи мультимодальной модели, состоящей из классификатора режимов и блока моделей режимов. Для каждого режима формируется собственная индуктивная база знаний, рассчитывается бинарная маска входов режима на основе отбора признаков и строится базовая модель режима. Классификатор режимов обучается в целях определения границ режима. Для повышения точности прогноза предлагается использование циклического обучения классификатора режимов и блока базовых моделей режимов. Идея циклического обучения состоит в попеременной итеративной настройке обеих частей мультимодальной модели, где результат прогноза одной части мультимодальной модели используется для обучения другой. Классификатор учится наиболее точно определять границы режимов процесса, а каждая базовая модель — наиболее точно описывать соответствующий ей режим. При прогнозе мультимодальной моделью выходных параметров с помощью классификатора режимов определяется режим для текущего такта с использованием соответствующей базовой модели. Проведено сравнение предложенного подхода к идентификации с популярными методами машинного обучения на реальных данных многорежимного процесса флотации железной руды. По результатам численного моделирования на тестовых данных процесса мультимодальная идентификационная модель продемонстрировала наибольшую точность прогноза.</p></abstract><trans-abstract xml:lang="en"><p>This paper proposes a new method for identification of technological processes with changing dynamics. This approach involves statistical analysis of dependencies between the inputs and outputs of the process. An algorithm for process modes identification is based on probabilistic latent analysis and EM algorithm. A process with changing dynamics is described using a multimodal model, which consists of a mode classifier and a block of basic mode models. For each mode, an inductive knowledge base is formed, a binary mask of mode inputs is calculated using feature selection, and a basic mode model is constructed. The mode classifier is trained to determine the boundaries of each mode. To improve forecast accuracy, this paper proposes using cyclical training of the mode classifier and the block of basic mode models. The idea of cyclic learning is to iteratively train both parts of the multimodal model, where the prediction result of one part of the multimodal model is used to train the other. The classifier learns to most accurately determine the boundaries of process modes, and each basic model learns to most accurately describe its corresponding mode. Mode is determined by mode classifier for the current state and the corresponding basic mode model is used to predict output parameters. The proposed approach was compared with popular machine learning methods using real data from a multimodal iron ore flotation process. Based on numerical simulation results using test process data, the multimodal identification model demonstrated the highest prediction accuracy.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>идентификация систем</kwd><kwd>машинное обучение</kwd><kwd>переменные режимы динамического процесса</kwd><kwd>латентный анализ</kwd><kwd>смесь распределений</kwd><kwd>отбор признаков</kwd></kwd-group><kwd-group xml:lang="en"><kwd>system identification</kwd><kwd>machine learning</kwd><kwd>changing process modes</kwd><kwd>latent analysis</kwd><kwd>mixture of distributions</kwd><kwd>feature selection</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Gur’eva E. M., Kol’tsov A. G. 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