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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">izvestswsu</journal-id><journal-title-group><journal-title xml:lang="ru">Известия Юго-Западного государственного университета</journal-title><trans-title-group xml:lang="en"><trans-title>Proceedings of the Southwest State University</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2223-1560</issn><issn pub-type="epub">2686-6757</issn><publisher><publisher-name>ЮЗГУ</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21869/2223-1560-2019-23-2-109-123</article-id><article-id custom-type="elpub" pub-id-type="custom">izvestswsu-498</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>Информатика и вычислительная техника</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Computer science, computer engineering</subject></subj-group></article-categories><title-group><article-title>К вопросу устойчивости прогнозирующей модели на основе кратномасштабного вейвлет-преобразования</article-title><trans-title-group xml:lang="en"><trans-title>To a Question of Predicting Model Stability on the Basis of Multiple Scale Wavelet Transformation</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>Сакрутина</surname><given-names>Е. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Sakrutina</surname><given-names>E. A.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Екатерина Алексеевна Сакрутина, научный сотрудник</p></bio><bio xml:lang="en"><p>Ekaterina A. Sakrutina, Researcher</p></bio><email xlink:type="simple">consoft@ipu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Федеральное государственное бюджетное учреждение науки Институт проблем управления им. В. А. Трапезникова Российской академии наук</institution></aff><aff xml:lang="en"><institution>Institute of Control Sciences named after V.A. Trapeznikov</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>09</day><month>07</month><year>2019</year></pub-date><volume>23</volume><issue>2</issue><fpage>109</fpage><lpage>123</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Сакрутина Е.А., 2019</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="ru">Сакрутина Е.А.</copyright-holder><copyright-holder xml:lang="en">Sakrutina E.A.</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://izvestswsu.elpub.ru/jour/article/view/498">https://izvestswsu.elpub.ru/jour/article/view/498</self-uri><abstract><sec><title>Цель исследования</title><p>Цель исследования. Настоящая работа посвящена проблеме создания прогнозирующих моделей производственных процессов и условиям их устойчивости.</p></sec><sec><title>Методы</title><p>Методы: Прогнозирующие модели активно применяются в современных системах управления, интеллектуальных системах информационной поддержки принятия решений, играют огромную роль в любой деятельности, связанной с процессами обработки сигналов, в том числе обнаружения аномалий различных технологических процессов и оценке рискового потенциала объектов критической информационной инфраструктуры, а также могут применяться в системах мониторинга угроз безопасности. Особый класс в ряду прогнозирующих моделей представляют собой модели, основанные на знаниях о протекающих процессах (например, закономерностях, извлекаемых из данных, накопленных в результате работы объекта).</p></sec><sec><title>Результаты</title><p>Результаты. В статье рассмотрена относящаяся к этому классу виртуальная «мгновенная» модель объекта, представленная с учетом кратно-масштабного разложения векторов входных воздействий и прогноза выхода объекта. Рассматриваемая модель дает прогноз без учета возможных будущих состояний прогнозного фона. Для исследования устойчивости виртуальной «мгновенной» модели разработан подход, основанный на вейвлет-анализе, который характеризуется уникальной возможностью детального частотного анализа во времени. На основе этого подхода получены условия устойчивости прогнозирующей модели с выделением условий для аппроксимирующей и детализирующей составляющих для четырех типов соотношений между глубиной памяти по входу и выходу.</p></sec><sec><title>Заключение</title><p>Заключение: В статье приведена прогнозирующая модель процесса нефтепереработки, в которой глубина памяти по входу больше глубины памяти по выходу. Показано, что точность прогноза виртуальной «мгновенной» модели выше, чем у линейной прогнозирующей модели при редких данных лабораторного анализа. Для построенной модели проиллюстрировано одно из условий устойчивости в зависимости от глубины разложения. На основе анализа полученных результатов можно сделать вывод о применимости полученных условий устойчивости для оценки рискового потенциала реализации прогноза развития процесса в системах мониторинга угроз безопасности.</p></sec></abstract><trans-abstract xml:lang="en"><sec><title>Purpose of research</title><p>Purpose of research. The article is devoted to the development of production predicting models and their stability conditions.</p></sec><sec><title>Methods</title><p>Methods: Predicting models are actively used in modern control systems, in information support intellectual systems of decision-making. They have a huge role in any activity connected with signals' processing including anomalies detection of various technological processes and assessment of risk potential of critical information infrastructure objects. They can also be used in monitoring systems of security threats. Special class among predicting models is represented by the models based on experiences of proceeding processes (for example, regularities taken from the data which are saved up as a result of an object work).</p></sec><sec><title>Results</title><p>Results. Virtual "instant" model of an object belonging to this class is described in the article. It is presented taking into account multiple and large-scale decomposition of entrance influences vectors and the forecast of an object output. The described model gives the forecast without possible future conditions of an expected background. The approach based on the wavelet-analysis which is characterized by a unique opportunity of detailed frequency analysis in time is developed for stability study of virtual "instant" model. Stability conditions of the predicting model are received on the basis of this approach. This model has allocation conditions for approximating and detailing components for four types of ratios between memory depth on input and output.</p></sec><sec><title>Conclusion</title><p>Conclusion: Predicting model of oil processing in which memory depth on an input is more than memory depth on output is described in the article. It is shown that the accuracy of virtual "instant" model forecast is higher than linear predicting model has at rare data of laboratory analysis. One of stability conditions depending on decomposition depth is shown for the constructed model. On the basis of received results analysis it is possible to draw a conclusion on applicability of received stability conditions for risk potential assessment of process development forecast implementation in monitoring systems of security threats.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>прогнозирующая модель</kwd><kwd>кратномасштабное вейвлет-преобразование</kwd><kwd>условия устойчивости</kwd><kwd>ассоциативный поиск</kwd><kwd>безусловный прогноз</kwd></kwd-group><kwd-group xml:lang="en"><kwd>predicting model</kwd><kwd>multiple scale wavelet transformation</kwd><kwd>stability conditions</kwd><kwd>associative search</kwd><kwd>unconditional forecast</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">Sakrutina E., Bakhtadze N. Towards the Possibility of Applying the Wavelet Analysis to Derive Predicting Models // IFAC-PapersOnLine. 2015. Vol. 48. Is. 1. 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