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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">gumrf</journal-id><journal-title-group><journal-title xml:lang="ru">Вестник Государственного университета морского и речного флота имени адмирала С. О. Макарова</journal-title><trans-title-group xml:lang="en"><trans-title>Vestnik Gosudarstvennogo universiteta morskogo i rechnogo flota imeni admirala S. O. Makarova</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2309-5180</issn><issn pub-type="epub">2500-0551</issn><publisher><publisher-name>ФГБОУ ВО «Государственный университет морского и речного флота имени адмирала С.О. Макарова»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.21821/2309-5180-2024-16-1-7-16</article-id><article-id custom-type="elpub" pub-id-type="custom">gumrf-416</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>Эксплуатация водного транспорта, водные пути сообщения и гидрография</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>OPERATION OF WATER TRANSPORT, WATERWAYS AND HYDROGRAPHY</subject></subj-group></article-categories><title-group><article-title>Определение местоположения судна по глубинам при помощи нейронной сети</article-title><trans-title-group xml:lang="en"><trans-title>Depth-based vessel position fixing by means of a neural network</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>Дерябин</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Deryabin</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Дерябин Виктор Владимирович — доктор технических наук, доцент</p><p>198035, Санкт-Петербург, ул. Двинская, 5/7</p></bio><bio xml:lang="en"><p>Deryabin, Viсtor V. — Dr. of Technical Sciences, associate professor</p><p>5/7 Dvinskaya Str., St. Petersburg, 198035</p></bio><email xlink:type="simple">gmavitder@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>ФГБОУ ВО «ГУМРФ имени адмирала С. О. Макарова»</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Admiral Makarov State University of Maritime and Inland Shipping</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>14</day><month>03</month><year>2024</year></pub-date><volume>16</volume><issue>1</issue><fpage>7</fpage><lpage>16</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Дерябин В.В., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Дерябин В.В.</copyright-holder><copyright-holder xml:lang="en">Deryabin V.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://journal.gumrf.ru/jour/article/view/416">https://journal.gumrf.ru/jour/article/view/416</self-uri><abstract><p>Предложен метод определения места судна по глубинам на основе нейронной сети, которая принимает на вход последовательность глубин, измеренных при помощи эхолота, а прогнозирует широту и долготу судна на момент измерения последней глубины. Нейронная сеть имеет архитектуру сети прямого распространения с несколькими скрытыми слоями и полными связями, удовлетворяющую условиям универсальной аппроксимации в соответствии с теоремой Стоуна – Вейерштрасса. Для обучения используется алгоритм Adamax при условии контроля наибольшего значения модуля невязки на каждой итерации. Моделирование выполнялось с использованием языка программирования Python и библиотеки Tensorflow. Модельная поверхность рельефа дна была представлена в виде многочлена второго порядка. Образцы получены на основе виртуальных измерений глубин в узлах координатной сетки с пространственным разрешением не хуже, чем один кабельтов. После сбора образцов выполнялось обучение нейронной сети, в ходе которого не использовалась контрольная выборка. В обучении участвовало несколько нейронных сетей, отличающихся количеством скрытых слоев, а также количеством нейронов в них. После обучения было проведено тестирование, которое предполагало движение судна вдоль меридианов, в точности не совпадающих с используемыми для формирования обучающей выборки. При этом наряду с вариантом средних по долготе меридианов рассмотрен вариант выбора меридианов с использованием датчика случайных чисел равномерного распределения. В результате тестирования все рассмотренные сети показали примерно одинаковую приемлемую навигационную точность, близкую к точности, полученной на обучающей выборке.</p></abstract><trans-abstract xml:lang="en"><p>A depth-based vessel position fixing method on the basis of a neural network is proposed. The network takes as an input a sequence of depth values measured by an echo-sounder and predicts vessel latitude and longitude for the moment of the latest depth measurement. The neural network has a fully-connected feedforward architecture with several layers which satisfies conditions of the universal approximation in compliance with the Stone-Weierstrass theorem. The Adamax algorithm for the neural network training with controlling a maximum value of position error at each epoch is implemented. Modeling is conducted with the Python programming language and the Tensorflow library. The model surface of seabed is performed as a second-order polynomial. Training samples on the basis of virtual soundings at the coordinate net knots with the space resolution not worse than one cable are obtained. After samples obtaining the training of the neural network is conducted. A validation set is not used. Several neural networks are trained. They have different number of hidden layers and different number of neurons per each hidden layer. After training the test procedure is performed. Test samples are generated in the assumption that a vessel is moving along meridians which are not used at the stage of the preliminary soundings survey. The cases of mean and random test meridians are considered. The random meridians are obtained with a uniform random number generator. As the result, all the tested neural networks have shown approximately identical navigational accuracy which is close to the accuracy for the training set.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>судно</kwd><kwd>местоположение</kwd><kwd>глубина</kwd><kwd>нейронная сеть</kwd><kwd>машинное обучение</kwd><kwd>автономный режим</kwd><kwd>рельеф дна</kwd><kwd>алгоритм расчета</kwd></kwd-group><kwd-group xml:lang="en"><kwd>vessel</kwd><kwd>position</kwd><kwd>depth</kwd><kwd>neural network</kwd><kwd>machine learning</kwd><kwd>autonomous mode</kwd><kwd>seabed relief</kwd><kwd>calculation algorithm</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">Клюева С. Ф. Синтез алгоритмов батиметрических систем навигации / С. Ф. Клюева, В. В. Завьялов. — Владивосток: Мор. гос. ун-т, 2013. — 132 с.</mixed-citation><mixed-citation xml:lang="en">Klyueva, S. F., and V. V. Zav’yalov. 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