and Computational Methods

doi: 10.18698/2309-3684-2017-3-83104

The study introduces an algorithm for classifying the aircraft surface elements based on a binary decision tree with threshold predicates. According to the initial description of the objects, we developed derived characteristics allowing for the classes to be separated with minimal losses. Moreover, we trained and verified the predicates on synthetic data and described an algorithm of obtaining the data for training. Low values of classification errors and ease of implementation make it possible to apply the algorithm for solving aerodynamic applied problems.

Kotenov V.P. ,Ratslav R.A. ,Sapozhnikov D.A. ,Chernyshev I.V. , A method for classifying aircraft surface elements for the numerical-analytical solution of aerodynamic problems .Маthematical Modeling and Computational Methods, 2017, №3 (15), pp. 83–104

doi: 10.18698/2309-3684-2019-3-100112

The paper considers a method for applying the analytical dependence to calculate the pressure on the surface of blunted cones in a supersonic gas flow at an angle of attack, taking into account the discontinuity in the generatrix curvature. To generalize the dependence on the case of three-dimensional flow, the method of local surfaces was used. The pressure coefficient on the surface of spherical bluntness is calculated separately from the conical part according to known ratios [1, 2]. The results were compared with empirical data and the results of accurate calculations in a strict mathematical formulation. The scope of applicability of the method is determined. From the comparison it follows that using the analytical formula for the pressure distribution on the surface of a blunted cone in three-dimensional flows in applied problems of aerodynamics allows significant simplifying calculations while maintaining good accuracy of the results.

Котенев В.П., Пучков А.С., Сапожников Д.А., Тонких Е.Г. Метод локальных поверхностей для моделирования давления на затупленном конусе при пространственном обтекании. Математическое моделирование и численные методы. 2019. № 3. с. 100–112.

doi: 10.18698/2309-3684-2018-4-5771

The paper introduces a neural network implemented to classify air frame surface ele-ments. Within the research, we generated a sample containing the surface parameters of classification objects. In order to avoid errors associated with different measurement scales, the criteria were scaled. According to synthetic data, the neural network was trained, and the proposed model was verified. The optimal configuration of the neural network was determined experimentally. As a criterion of optimality, we used the proportion of correct answers from the test and training samples, and carried out calibration and modification of individual model parameters. The classification results of the test sample by the optimal network were summarized in the error matrix. The most significant result was achieved when distinguishing the class of ellipsoids. Separate blocks of the matrix show that the neural network accurately distinguishes the classes of ellipsoids and hyperboloids. The study proposes some ideas for further modification of the algorithm in order to increase the proportion of correct answers when distinguishing the class of paraboloids.

Булгаков В.Н., Рацлав Р.А., Сапожников Д.А., Чернышев И.В. Моделирование нейронной сети для решения задачи классификации элементов корпуса летательного аппарата. Математическое моделирование и численные методы, 2018, № 4, с. 57–71.

doi: 10.18698/2309-3684-2017-2-8193

The article presents an analytical expression for calculating pressure on the surface of blunted cones in a supersonic gas flow, taking into account the curvature discontinuity along the generatrix. We used a genetic algorithm and multi-stage functional optimisation methods for the least-squares method to determine free parameters of the expression. We compare the results obtained to the rigorous numerical solution to the inviscid problem. The comparison shows that it is possible to use the analytical expression for pressure distribution over a surface in a wide Mach number range for various cone halfangles. The expression proposed accounts for the curvature discontinuity along the generatrix at the point where the sphere is tangent to the conical surface, unlike the expressions found in previously published works.

Bulgakov V.N., Kotenev V.P., Sapozhnikov D.A. Modeling supersonic flow around blunted cones, taking into account the curvature discontinuity along the generatrix of the solid. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 81-93

doi: 10.18698/2309-3684-2017-4-6072

The article introduces a dependency for the pressure distribution in the disturbed region near the sphere streamlined by the flow of the supersonic inviscid gas, obtained when modifying the Shepard’s Method. We use known ratios for the pressure on the body and the shockwave as well as data from the numerical experiments. We have compared the results with the data not used in the learning process of the dependency coefficients. This comparison proves high confidence of the model obtained.

Kotenev V.P., Puchkov A.S., Sapozhnikov D.A., Tonkikh E.G. Simulation 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, №4 (16), pp. 60-72

doi: 10.18698/2309-3684-2018-2-109121

The generalization of the dependency which was proposed earlier for determining of the pressure in perturbed area streamlined by the supersonic flow of the inviscid perfect gas was provided. The modification allows to consider effects which occur when the sphere is streamlined by high temperature gas with adiabatic index which do not equal 1.4. According to article [2-3], made adjustment to the function which describes the behavior of the shock wave which depends on the adiabatic index. The Shepard function’s coefficient also consider of adiabatic index. First and second order members of Shepard function which describe a pressure in area does not change. Comparison of application versions with the available data calculations for the high temperature gas and approximations based on perfect gas shows high accuracy of the proposed approach.

Котенев В.П., Пучков А.С., Сапожников Д.А., Тонких Е.Г. Восстановление распределения давления в возмущенной области около сферы, обтекаемой сверхзвуковым потоком газа с произвольным эффективным показателем адиабаты. Математическое моделирование и численные методы, 2018, № 2, с. 109–121