### Rubric: "1.2.2. Mathematical modeling, numerical methods and software packages (technical sciences)"

#### 551.513 Global climate model taking into account the biogeochemical carbon cycle of terrestrial vegetation

##### Parkhomenko V. P. (ФИЦ ИУ РАН/Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2021-2-3853

The aim of this work is to consider a global model of the carbon cycle. The model describes the production process of forest ecosystems taking into account the seasonal sicle of climatic factors. It is designed to simulate a long period of time as part of a global climate model of intermediate complexity. It has been established that the global characteristics of the climate system reach a steady state over a period of about 2000 years, and the model works steadily. The temporal and spatial distributions of the obtained climatic characteristics and the biogeochemical carbon cycle of terrestrial vegetation are given.

Пархоменко В.П. Глобальная климатическая модель с учетом биогеохимического углеродного цикла растительности суши. Математическое моделирование и численные методы, 2021, № 2, с. 38–53.

#### 519.654 Modeling of cyclic processes (of time series type experimental date) by solution of piecewise linear differential equations with constant coefficients

##### Smirnov V. Y. (LTD Azforus/MONIKI), Kuznetsova A. V. (IBCP RAS)

doi: 10.18698/2309-3684-2022-4-6380

This paper presents a method for modeling of real macroworld cyclic processes by the solutions of two (or more) linear differential equations with constant coefficients. It is shown that possible to send such model from any initial condition (point in phase space) to a prescribed final point in phase space for a prescribed amount of steps. As a result, conditions for a constructing closed cycle in phase space of any dimension were found. Switching from one system of equations to another is obtained then integral curve reaches some threshold — frontier in phase sheet (space). The analysis of convergence rate of the solution for such closed cycles is made. The integral curve behavior significant dependence of initial condition was shown.The obtained model is connected with experimental data in the form of time series and approximates them with solution of linear differential equations on condition of minimizing the RMS deviation. Proposed model also can be applied to a task of some index (technical, economical) reaching the prescribed meaning to a prescribed moment.

Смирнов В.Ю., Кузнецова А.В. О моделировании циклических процессов решениями кусочно-линейных разностных уравнений с постоянными коэффициентами по экспериментальным данным в виде временных рядов. Математическое моделирование и численные методы, 2022, № 4, с. 63–80.

#### 621.464.3 Mathematical modeling hydraulic systems for synchronous movement of actuators based on a throttle flow divider

##### Bushuev A. Y. (Bauman Moscow State Technical University), Danilov N. A. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2022-2-313

A mathematical model of functioning of synchronization systems of actuators based on a throttle flow divider was developed to solve design problem. The solution of the optimization problem of a mismatch time of movement of actuators operating under conditions of external alternating-sign force effects is given, performed using the genetic algorithm and refined using the Nelder-Mead algorithm

Бушуев А.Ю., Данилов Н.А. Математическое моделирование гидравлической системы синхронизации исполнительных органов на основе дроссельного делителя потока. Математическое моделирование и численные методы, 2022, № 2, с. 3–15

#### 519.6 Numerical solution of equations of mixed type in unlimited region on a plane

##### Galanin M. P. (Bauman Moscow State Technical University/Keldysh Institute of Applied Mathematics of the Russian Academy of Scienсes), Ukhova A. R. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2023-3-105124

The purpose of the work is to build and implement an algorithm for finding a numerical solution to a problem for mixed-type equations in an unlimited region. In this case problems are considered in which the process under study is described in some limited area by the thermal conductivity equation or wave equation, and outside it by the Laplace equation. The necessary additional conditions at zero, at infinity and the conditions for conjunction at the border of the inner region are set. There is described an algorithm for finding a numerical solution to a problem with a wave equation in a limited region in one-dimensional and two-dimensional cases, problems with a thermal conductivity equation or a wave equation in a two-dimensional case. Difference schemes are built by the integro–interpolation method. The task is solved in a limited area. Nonlocal boundary conditions are set on its border so the solution of task in limited area coincides with projection of problem in unlimited area. In this case, an artificial boundary is introduced for the solution in the part of the region in which the process is described by the Laplace equation. An iterative algorithm and an algorithm with a non-local boundary condition are built. The results of calculations for examples in various fields are presented.

Галанин М.П., Ухова А.Р. Численное решение уравнений смешанного типа в неограниченной области на плоскости. Математическое моделирование и численные методы, 2023, № 3, с. 105–124.

#### 519.8 A "mixed" model of the confrontation of numerous groups with linear dependencies on the time of the effective speed of strikes by units of the parties

##### Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2022-2-102113

Using the method of dynamics of averages, a "mixed" model of numerous groupings confrontation has been developed with linear dependencies on the time of effective speeds of striking by units of the parties. An algorithm is constructed that allows to investigate the course of the process and calculate its main indicators. It is established that the use of confrontation models with constant effective speed of strikes in many cases leads to significant errors in the calculation of the main indicators of the process. The influence of a preemptive strike by one of the opposing sides on the course of the progress and the final outcome are investigated.

Чуев В.Ю., Дубограй И.В. «Смешанная» модель противоборства многочисленных группировок при линейных зависимостях от времени эффективных скоростей воздействий единицами сторон. Математическое моделирование и численные методы, 2022, № 2, с. 104–115

#### 004.855.5 Neural network methods for solving the problem of credit scoring

##### Kadiev A. D. (Bauman Moscow State Technical University), Chibisova A. V. (Bauman Moscow State Technical University)

doi: 10.18698/2309-3684-2022-4-8192

The mathematical derivation of the presented neural network model is demonstrated. Reduction of the classification problem to an optimization problem. Produced recon-naissance data analysis, as well as their preprocessing for further use in training classification algorithms. The architectures of neural networks were designed depending on the activation function, the number of hidden layers of the neural network and the number of neurons in the hidden layers. More than ten neural networks were trained to solve the task of credit scoring. The calculation of the learning time of neural networks was made. The solution of the problem using classical machine learning algorithms is presented. It could be seen that the standard deviation of accuracy and ROC AUC for neural networks is greater than that of a random forest. This is due to the fact that we choose the initial weights randomly and calculate the gradients not on the entire sample, but on small parts, which adds some learning error. But these deviations were not only for the worse. In the best situations, according to both metrics, neural networks showed the worst result by a couple of percent. The analysis of results is made. Comparative analysis shows that neural networks have better classification quality than classical machine learning algorithms, and also that neural networks have less training time than classical machine learning algorithms. Graphs and tables displaying the results obtained are presented.

Кадиев А.Д., Чибисова А.В. Нейросетевые методы решения задачи кредитного скоринга. Математическое моделирование и численные методы, 2022, № 4, с. 81–92.

#### 519.6:621.791.05+544.015.4 Investigation of the effect of wettability and concentration of modifying nanoparticles on the weld structure in laser welding of an aluminum alloy

##### Isaev V. I. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS), Cherepanov A. N. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS), Shapeev V. P. (Khristianovich Institute of Theoretical and Applied Mechanics SB RAS/Новосибирский государственный университет)

doi: 10.18698/2309-3684-2023-1-8191

We proposed a self-consistent thermokinetic model of binary alloy crystallization in the weld joint modified by nanodimensional inoculators added to the welding pool during the laser weling process. This combined model of laser welding of uniform metals describes thermophysical prcesses of macroscopic properties of the weld joint and its structure depending on welding regimes and properties of nanomodifying powders (capillary angle, powder concentration). It is based on a thermophysical model of the action of the laser radiation on metal during the laser welding of metallic plates. The simulation is supplemented with a nonequilibrium model of heerogeneous nucleation and the growth of crystalline phase on nanomodifying particles added to the welding pool during the cooling and solidification of alloy in the weld joint. Numerical simulations based on the collocations and least squared methods were performed for butt weling of plates made of a binary aluminum alloy. We calculated the temperature distribution in the plates, the shape of the cross-section of the welding pool, and quantitative properties of its crystal structure. We investigated the effect of the capillary angle and nanomodifying powder concentration on the crystal grain size

Исаев В.И., Черепанов А.Н., Шапеев В.П. Исследование влияния смачиваемости и концентрации модифицирующих наночастиц на структуру шва при лазерной сварке алюминиевого сплава. Математическое моделирование и численные методы, 2023, No 1, с. 81–91.

#### 621.822.2, 519.63 Numerical study of the influence of lubricant viscosity grade on thrust bearing operation

##### Sokolov N. V. (HMS Compressors Business Unit (HMS Group)/Казанский национальный исследовательский технологический университет), Khadiev M. B. (Казанский национальный исследовательский технологический университет), Fedotov P. E. (Kazan (Volga region) Federal University,/LLC «AST Volga region»), Fedotov E. M. (LLC «AST Volga region»)

doi: 10.18698/2309-3684-2023-1-92111

The study of the influence of the viscosity grade of the supplied oil ISO VG32 and ISO VG46 in a wide range of rotor speeds and operating clearances on the local and integral characteristics of a thrust plain bearing with fixed pads of the compressor is presented. The studies were carried out using the Sm2Px3Txτ calculation program based on the results of numerical experiments of the bearing. The program is built by numerical implementation of a nonstationary periodic thermoelastohydrodynamic (PTEHD) mathematical model of the thrust bearing operation. The research results indicate a significant influence of the oil viscosity grade on the main characteristics and temperature conditions of the thrust bearing. When changing from ISO VG46 to the lighter oil ISO VG32, there is a noticeable reduction in bearing pad temperatures and power loss. However, the level of this change is determined by the specified operating clearance between the rotating thrust collar and the bearing pads. The influence of oil viscosity grade and the profile of the working surface on the temperature regime of the pad is analyzed. The value and location of the maximum temperature of the thrust bearing pad is determined, as well as the possibility of applying the standard point 75/75 from API-670 in practice.

Соколов Н.В., Хадиев М.Б., Федотов П.Е., Федотов Е.М. Численное исследование влияния класса вязкости смазки на работу упорного подшипника скольжения. Математическое моделирование и численные методы, 2023, No 1, с. 92–111.

#### 338.001.36 Mathematical model for the formation of supply chains of raw materials from the commodity exchange under risk based on the profit trajectory for previous periods redundancy

##### Rogulin R. S. (Vladivostok State University)

doi: 10.18698/2309-3684-2023-2-129154

The formation of the supply chain of raw materials is closely related to the production problems of woodworking enterprises. Construction of supply chains for raw materials and the optimal calculation of daily production have been hot topics since the beginning of the second industrial revolution. This article discusses the enterprise of the Primorsky Territory of the woodworking industry, which does not have plots for rent. The purpose of the work is to solve the problem of building a supply chain of raw materials, taking into account the daily loading of production facilities and finding the optimal solution. The source of raw materials is the commodity exchange, where lots appear daily randomly in different mining regions. In the scientific literature, there are many ways to calculate the best profit value, taking into account many restrictions, but they do not take into account many features that are important for woodworking enterprises. Based on a review of the scientific literature, this article presents a mathematical model that acts as a decisionmaking mechanism on each individual day, and it differs in that it can take into account the coefficient of useful volume of raw materials that will reach the warehouse and travel time. The model was tested on the data of the Russian Commodity and Raw Materials Exchange and a company in Primorsky Krai. The result of testing the model is the calculated optimal profit trajectory for each set of data on the volume of raw materials, the time of lots in transit, as well as many important indicators for any production: profit volume, production volume of goods. The analysis of the received solutions showed that there are difficulties in planning supply chains and production volumes. The regions are analyzed as sources of raw materials, from which regions and when it is worth buying raw materials. The shortcomings and positive aspects of the mathematical model are given

Рогулин Р.С. Математическая модель формирования цепочек поставок сырья с товарно-сырьевой биржи в условиях риска с опорой на траекторию прибыли за предыдущие периоды. Математическое моделирование и численные методы, 2023,№ 2, с. 129–154.