doi: 10.18698/2309-3684-2025-4-173193
The article considers the neural network approach to solving the inverse problem of generating surface waves or identifying a disturbance source based on data taken from the free surface of a liquid. The type is selected and a mathematical and computer model of the neural network is constructed based on data obtained during a laboratory experiment to study surface waves that occur when an airfoil and a circular cylinder move in a liquid. To assess the adequacy of this model, numerical experiments are conducted to determine the depth and velocity of the disturbance source in the liquid. The calculation results are compared with the experimental data. A software package has been developed that allows one to effectively and with minimal time expenditure solve the problem of determining the parameters of the disturbance source based on data taken from the water surface.
[1] Nesterova S.V., SHamaeva A.S., SHamaeva S.I. Metody, procedury i sredstva aerokosmicheskoj komp'yuternoj radiotomografii pripoverhnostnyh oblastej Zemli [Methods, procedures and means of aerospace computed radio tomography of the near-surface regions of the Earth.]. Moscow, «Nauchny Mir» Publishers, 1996, 272 p.
[2] Savin A.S. Opredelenie parametrov gidrodinamicheskih osobennostej v ploskom potoke po dannym o ego svobodnoj poverhnosti [Determination of the parameters of hydrodynamic features in a flat flow from data on its free surface]. Fluid Dynamics, 2001, no. 2, pp. 139–146.
[3] Tihonov A.N., Arsenin V.YA. Metody resheniya nekorrektnyh zadach [Methods for solving ill-posed problems]. Moscow, Nauka Publ., 1979, 286 p.
[4] Konovalov A.V., Levchenko E.S., Savin A.S. Vosstanovlenie ploskogo techeniya tyazheloj ideal'noj zhidkosti po forme ee svobodnoj poverhnostiyu [Reconstruction of the plane flow of a heavy ideal fluid from the shape of its free surface]. Doklady Akademii Nauk SSSR [Proceedings of the USSR Academy of Sciences], 1989, vol. 305, no. 2, pp. 294 – 296.
[5] Isichenko I.V., Konovalov A.V., Levchenko E.S., Savin A.S. Obratnaya zadacha obtekaniya osobennostej ploskim potokom ideal'noj zhidkosti so svobodnoj granicej [The inverse problem of a plane flow of an ideal fluid with a free boundary past singularities]. Journal of Applied Mechanics and Technical Physics, 1989, no. 6, pp. 86 – 91.
[6] Voronin E. A., Nosov V. N., Savin A. S. Neural network approach to solving the inverse problem of surface-waves generation. Journal of Physics: Conference Series. 2019, 1392, vol. 1, art. 012022. DOI: 10.1088/1742-6596/1392/1/012022.
[7] Voronin E.A., Nosov V.N., Savin A.S. Determination of submerged source parameters from liquid surface disturbances based on machine learning methods. Doklady Earth Sciences, 2020, vol. 493, no. 1, pp. 103-106.
[8] Agarval CH. Nejronnye seti i glubokoe obuchenie: uchebnyj kurs [Neural networks and deep learning: training course]. St. Petersburg, Dialektika [Dialectics LLC], 2020, 752 p.
[9] Prosiz Dzh. Prikladnoe mashinnoe obuchenie i iskusstvennyj intellekt dlya inzhenerov [Applied machine learning and artificial intelligence for engineers]. Astana, Alist, 2024, 432 p.
[10] Khaikin S. Neural networks: a complete course, 2nd ed. Moscow, Williams Publishing House, 2006, 1104 p.
[11] Manning C., Raghavan P., Schutze H. Introduction to Information Retrieval. Cambridge University Press, 2009, 544 p.
[12] Kuhn M., Johnson K. Applied predictive modeling. New York, Springer, 2013, 600 p.
[13] Nathan M., James W. Big Data: Principles and best practices of scalable realtime data systems. Manning Publications, 2015, 308 p.
[14] Raschka S. Python and Machine Learning. Birmingham, Packt Publishing, 2017, p. 418.
[15] Serrano L. Grokking Machine Learning [Grokaem machine learning]. St. Petersburg, Piter [Piter Publishing House], 2024, 512 p.
[16] Murphy K.P. Probabilistic Machine Learning: Advanced Topic. Cambridge, MITP Press, 2022, 770 p.
[17] Postolit A.V. Osnovy iskusstvennogo intellekta v primerah na Python. Samouchitel'. 2-e izd [Basics of artificial intelligence with examples in Python. Self-instruction manual. 2nd ed.]. St. Petersburg, BHV-Petersburg, 2024, 448 p.
[18] Boyarincev V.I., Lednev A. K., Frost V.A. Dvizhenie pogruzhennogo cilindra pod poverhnost'yu zhidkosti. Preprint [Movement of a submerged cylinder under the surface of a liquid. Preprint]. Moscow, Institut problem mekhaniki AN SSSR [Institute of Mechanical Problems of the USSR Academy of Sciences], 1988, no. 332, 39 p.
[19] Boyarincev V.I., Lednev A.K., Prudnikov A.S., Savin A.S., Savina E.O. Modelirovanie i eksperimental'noe issledovanie vozmushchenij svobodnoj granicy ploskogo potoka pogruzhennymi istochnikami. Preprint [Modeling and experimental study of disturbances of the free boundary of a plane flow by immersed sources. Preprint]. Moscow, Institut problem mekhaniki AN SSSR [Institute of Mechanical Problems of the USSR Academy of Sciences], 2002, no. 720, 37 p.
[20] Boyarincev V.I., Lednev A.K., Prudnikov A.S., Savin A.S., Savina E.O. Vozmushchenie svobodnoj poverhnosti zhidkosti krylovym profilem [Disturbance of the free surface of a liquid by an airfoil]. Fluid Dynamics, 2004, no. 6, pp. 145- 152.
[21] Barmin A.A., Boyarincev V.I., Lednev A.K., Savin A.S., Savina E.O. Modelirovanie i eksperimental'noe issledovanie vozmushchenij svobodnoj poverhnosti zhidkosti sharom i ellipsoidom. Preprint [Modeling and experimental study of perturbations of the free surface of a liquid by a ball and an ellipsoid. Preprint]. Moscow, Institut problem mekhaniki AN SSSR [Institute of Mechanical Problems of the USSR Academy of Sciences], 2004, no. 763, 43 p.
[22] Kotenev V.P., Puchkov A.S., Sapozhnikov D.A., Tonkikh E.G. imulation of the pressure distribution in the disturbed region near the sphere streamlined by the inviscid flotation by means of the machine learning methods. Mathematical Modeling and Computational Methods, 2017, no. 4, pp. 60–72.
[23] Bulgakov V.N., Ratslav R.A., Sapozhnikov D.A., Chernyshev I.V. Modeling a neural network to solve the problem of classifying air frame elements. Mathematical Modeling and Computational Methods, 2024, no. 3, pp. 81–99.
[24] Kreerenko S.S., Kreerenko S.S. Parametric identification of aerodynamic characteristics of a transport category aircraft using recurrent semi-empirical neural networks in the Tensorflow environment. Mathematical Modeling and Computational Methods, 2024, no. 3, pp. 81–99.
Воронин Е.А., Носов В.Н., Савин А.С. Нейросетевой подход к решению обратной задачи генерации поверхностных волн. Математическое моделирование и численные методы, 2025, № 4, с. 173–193.
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