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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">msi</journal-id><journal-title-group><journal-title xml:lang="ru">Современная наука и инновации</journal-title><trans-title-group xml:lang="en"><trans-title>Modern Science and Innovations</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2307-910X</issn><publisher><publisher-name>North-Caucasus Federal University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.37493/2307-910X.2025.4.3</article-id><article-id custom-type="elpub" pub-id-type="custom">msi-1778</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>ТЕХНИЧЕСКИЕ НАУКИ. ИНФОРМАТИКА, ВЫЧИСЛИТЕЛЬНАЯ ТЕХНИКА И УПРАВЛЕНИЕ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>TECHNICAL SCIENCES. INFORMATION, COMPUTING AND MANAGEMENT</subject></subj-group></article-categories><title-group><article-title>Комплексная модель обнаружения аномалий в распределённых системах с применением спектральных и биометрических методов</article-title><trans-title-group xml:lang="en"><trans-title>Comprehensive anomaly detection model for distributed systems using spectral and biometric methods</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0002-4186-7412</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Калиберда</surname><given-names>И. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kaliberda</surname><given-names>I. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Калиберда Игорь Владимирович – старший преподаватель, Пятигорский институт (филиал) Северо-Кавказского федерального университета.</p><p>Ул. Ермолова, 46, г. Пятигорск, Ставропольский край, 357500</p></bio><bio xml:lang="en"><p>Igor V. Kaliberda – Senior Lecturer, Pyatigorsk Institute of the North Caucasus Federal University.</p><p>46 Yermolova Street, Pyatigorsk, Stavropol Territory, 357500</p></bio><email xlink:type="simple">kaliberda-igor@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Северо-Кавказский федеральный университет, Пятигорский институт (филиал) СКФУ</institution><country>Россия</country></aff><aff xml:lang="en"><institution>North-Caucasus Federal University, Pyatigorsk Institute (branch) of NCFU</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>26</day><month>01</month><year>2026</year></pub-date><volume>0</volume><issue>4</issue><fpage>37</fpage><lpage>46</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Калиберда И.В., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Калиберда И.В.</copyright-holder><copyright-holder xml:lang="en">Kaliberda I.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://msi.elpub.ru/jour/article/view/1778">https://msi.elpub.ru/jour/article/view/1778</self-uri><abstract><sec><title>Введение</title><p>Введение. В статье рассмотрена интеграция спектрального анализа сетевого поведения и современных биометрических методов аутентификации.</p></sec><sec><title>Цель</title><p>Цель. Целью исследования является повышение безопасности распределённых вычислительных систем. Перспективы дальнейших исследований включают использование вейвлет-преобразований для анализа нестационарных трафиков, адаптацию порогов обнаружения в зависимости от контекста пользователя.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. Модель включает использование рядов Фурье для анализа периодичности сетевых процессов, а также применение FaceNet, VGGFace и IrisCode для корректной идентификации пользователей. Представлена корреляционная модель, объединяющая биометрические и спектральные характеристики пользователя, позволяющая формировать интегральный показатель риска. Результаты и обсуждение. Проведён численный анализ, демонстрирующий возможность разделения нормальных пользователей и злоумышленников по спектральным характеристикам поведения. Графические результаты подтверждают эффективность предлагаемой модели.</p></sec><sec><title>Заключение</title><p>Заключение. По итогам проведенного исследования можно сделать вывод о том, что применение разложения в ряды Фурье позволяет формализовать поведенческий профиль пользователя в частотной области и выявлять высокочастотные компоненты, характерные для автоматизированных атак.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Introduction</title><p>Introduction. The article discusses the integration of spectral analysis of network behavior and modern biometric authentication methods.</p></sec><sec><title>Goal</title><p>Goal. The goal of the research is to improve the security of distributed computing systems. Further research prospects include the use of wavelet transformations for analyzing non-stationary traffic, and the adaptation of detection thresholds based on the user's context.</p></sec><sec><title>Materials and methods</title><p>Materials and methods. The model includes the use of Fourier series to analyze the periodicity of network processes, as well as the use of FaceNet, VGGFace, and IrisCode for the correct identification of users. A correlation model is presented that combines the biometric and spectral characteristics of a user, allowing for the formation of an integrated risk indicator.</p></sec><sec><title>Results and discussion</title><p>Results and discussion. A numerical analysis has been conducted to demonstrate the possibility of separating normal users and attackers based on the spectral characteristics of their behavior. The graphical results confirm the effectiveness of the proposed model.</p></sec><sec><title>Conclusion</title><p>Conclusion. Based on the results of this study, it can be concluded that the use of Fourier series decomposition allows for the formalization of a user's behavioral profile in the frequency domain and the identification of high-frequency components characteristic of automated attacks.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>распределённые системы</kwd><kwd>безопасность</kwd><kwd>обнаружение аномалий</kwd><kwd>спектральный анализ</kwd><kwd>ряды Фурье</kwd><kwd>биометрическая аутентификация</kwd><kwd>FaceNet</kwd><kwd>VGGFace</kwd><kwd>IrisCode</kwd><kwd>поведенческий анализ</kwd><kwd>сетевой трафик</kwd><kwd>корреляционная модель риска</kwd><kwd>Fourier-спектр</kwd><kwd>IDS</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Distributed systems</kwd><kwd>Fourier analysis</kwd><kwd>biometric authentication</kwd><kwd>FaceNet</kwd><kwd>IrisCode</kwd><kwd>VGGFace</kwd><kwd>spectral anomaly detection</kwd><kwd>network traffic modeling</kwd><kwd>intrusion detection systems</kwd><kwd>user behavior profiling</kwd><kwd>ROC optimization</kwd><kwd>information security</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">Оппенгейм А. 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