The purpose of this work is to study the applicability of the U-Net architecture for automatically determining the contours of natural skins using the TensorFlow and Keras libraries in Python. A software application has been developed based on methods including OpenCV libraries, as well as a model for implementing a deep convolutional neural network. The dataset for training and testing the network was created using augmentation. Training was carried out using the stochastic gradient descent method after splitting the data sample into training and test images. In the future, the results obtained will be used to create an automated system that will make it possible to determine the contours of the skin and its defects, which in turn will open up the possibility of calculating the useful area of ​​the skin and creating an automated layout of patterns taking into account the identified defects.

Keywords: computer vision, edge detection, natural skin, machine learning, convolutional neural networks, U-Net architecture, deep learning

The rocks that form a natural geological reservoir for underground gas storage, during the operation of UGS, are exposed to prolonged cyclic loads caused by periodic injections and withdrawals of natural gas. At the same time, it is possible to develop and accumulate residual deformations in rocks that cause irreversible changes in the properties of rocks and this must be taken into account when designing and operating UGS.

Keywords: underground gas storage, geomechanical modeling, cavern, salt massif, deformations

the work is devoted to a comparative analysis of various calculation and mathematical models among themselves. The calculation of the frame joint of reinforced concrete structures is performed: a pylon and a cantilever beam. Three methods for performing the calculation of this joint are proposed: an analytical method, a rod FEM model and a volumetric FEM model. The analysis of the calculation results is performed: a comparison of internal forces and calculated reinforcement. The consequences of a superficial analysis of the structure and simplification of calculation models are shown using the example of damage to a real structure under the action of operational loads.

Keywords: reinforced concrete console, structure calculation, node calculation, Lira 10, Russian software, optimal design of reinforced concrete structures, reinforcement analysis

A mathematical model for managing a commercial organization that specializes in the production and sale of asphalt and asphalt concrete is presented and analyzed in this paper. The study is based on mathematical modeling principles and management theory. An organized two-tier management system has been proposed, consisting of an asphalt manufacturer and its clients. The problem was considered numerically using various types of input data, and the company "FIRM PROFILE LLC" provided necessary information for calculations. The paper analyzes the results obtained and offers practical recommendations for improving the management of this enterprise.

Keywords: optimal management, mathematical modeling, simulation modeling, enterprise model, hierarchical system

This paper discusses the influence of the turbulence model selection in predicting heat transfer in tube bundles in two- and three-dimensional settings. Numerical studies were performed for in-line and staggered tube bundles using Ansys Fluent software with three RANS turbulence models (k-ω SST, RSM EWT, and RNG k-ε) and a laminar solver. The tube lengths l in three dimensions were 0.5D and 3D, with a fixed tube diameter D. The Reynolds number Re ranged from 100 to 2900. The results showed that the turbulence model selection affects the qualitative flow pattern in tube bundles, with two-dimensional structures predominating in the flow regardless of the turbulence model selection. Therefore, the tube length has virtually no effect on the ability to predict heat transfer intensity. It is shown that when using the laminar solver, the effect of the bundle tube length can be significant depending on Re and the bundle layout. Good agreement with experimental data is obtained for the RSM EWT and RNG k-ε EWT models. For a staggered bundle, when choosing the k-ω SST model, satisfactory agreement with experimental data is observed, while the heat transfer of the in-line bundle is significantly underestimated. The use of the laminar solver in a steady-state formulation is justified for a pronounced laminar flow, at Re < 1000 with a further increase in Re, it is necessary to use a unsteady formulation with sufficient time and mesh resolution.

Keywords: convective heat transfer, in-line tube bundle, staggered tube bundle, computational simulation, turbulence modeling

The article deals with multi-criteria mathematical programming problems aimed at optimizing food production. One of the models of one-parameter programming is associated with solving the problem of combining crop production, animal husbandry and product processing. It is proposed to use the time factor as the main parameter, since some production and economic characteristics can be described by significant trends. The second multi-criteria parametric programming model makes it possible to optimize the production of agricultural products and harvesting of wild plants. in relation to the municipality, which is important for territories with developed agriculture and high potential of food forest resources.

Keywords: parametric programming, agricultural production, two-criteria model

The work is devoted to the study of the temperature distribution and equivalent voltage on the surface of a thermal radiation receiver during experimental and computational series. The experiments showed a qualitative and quantitative coincidence of the temperature data obtained by thermal imaging with the results of numerical modeling. The average error was 0.5℃, with a maximum deviation of 1.5℃ at individual points, which is due to edge effects and thermal insulation features. The computational model reproduces the main characteristics of the temperature field, including the effect of shielding, using a relatively low density of the computational grid. As part of the verification of the numerical model, the analysis of grid convergence was carried out, as well as the control of residuals and control of solution parameters were performed.

Keywords: heat exchanger, numerical and analytical calculation, convective and radiant heat transfer, efficiency improvement, outgoing flue gas, heat recovery, gas-liquid heat exchanger, numerical modeling, mathematical model, ANSYS Workbench software

The use of simulation analysis requires a large number of models and computational time. Reduce the calculation time in complex complex simulation and statistical modeling, allowing the implementation of parallel programming technologies in the implemented models. This paper sets the task of parallelizing the algorithmization of simulation modeling of the dynamics of a certain indicator (using the example of a model of the dynamics of cargo volume in a storage warehouse). The model is presented in the form of lines for calculating input and output flows, specified as: a moving average autoregressive model with trend components; flows of the described processes, specified according to the principle of limiting the limitation on the volume (size) of the limiting parameter, with strong stationarity of each of them. A parallelization algorithm using OpenMP technology is proposed. The efficiency indicators of the parallel algorithm are estimated: speedup, calculated as the ratio of the execution time of the sequential and parallel algorithm, and efficiency, reflecting the proportion of time that computational threads spend in calculations, and representing the ratio of the speedup to the sequential result of the processors. The dependence of the execution of the sequential and parallel algorithm on the number of simulations has been constructed. The efficiency of the parallel algorithm for the main stages of the simulation implementation was obtained at the level of 73%, the speedup is 4.38 with the number of processors 6. Computational experiments demonstrate a fairly high efficiency of the proposed parallel algorithm.

Keywords: simulation modeling, parallel programming, parallel algorithm efficiency, warehouse loading model, OpenMP technology

The problem of planning the sending of messages in a cellular network to destinations with known needs is considered. It is assumed that the costs of transmitting information on the one hand are proportional to the transmitted volumes and the cost of transmitting a unit of information over the selected communication channels in cases of exceeding the traffic established by the contract with the mobile operator, and on the other hand are associated with a fixed subscription fee for the use of channels, independent of the volume of information transmitted. An indicator of the quality of the plan in this setting is the total cost of sending the entire planned volume of messages. A procedure for reducing the formulated problem to a linear transport problem is proposed. The accuracy of the solution obtained on the basis of the proposed algorithm is estimated.

Keywords: single jump function, transport problem, minimum total cost criterion, computational complexity of the algorithm, confidence interval

In this paper, the problem of an equalizer design for high-speed receiver channel which is designed to compensate for the uneven frequency response of the input differential signal. Using special design methods, as well as modeling tools for frequency and transient characteristics, an equalizer with the ability to digitally adjust the gain was developed. This adjustment also reduces the impact of the spread of process parameters, which is inevitable during the production of the chip.

Keywords: attenuation, transceiver, equalizer, IP block, equalization, gain, amplitude

It is propossed to use foggy calculations to reduce the load on data transmission devices and computing systems in GIS. To improve the accuracy of estimating the efficiency of foggy calculations a non-Markov model of a multichannel system with queues, "warming up" and "cooling" is used. A method for calculating the probalistic-temporal characteristics of a non-Markov system with queues and with Cox distributions of the duration of "warming up" and "cooling" is prorosed. A program has been created to calculate the characteristics of the efficiency of fog calculations. The silution can be used as a software tool for predictive evaluation of the efficiency of access to geographic information systems, taking into account the features of fog computing technology and the costs of ensuring information security.

Keywords: fog computing, model of a multi-channel service system with queues, “warming up”, “cooling down”, geographic information systems, Cox distribution

The paper discusses a method for constructing a nonlinear software reliability efficiency function. The proposed algorithm is based on the use of information about the values ​​of reliability criteria, as well as some expert judgments. This approach differs significantly from previously proposed models for assessing software reliability, which are based on a probabilistic approach. In the proposed method, in addition to objective information, subjective expert assessments are taken into account, which allows for a more flexible assessment of the reliability of software products.

Keywords: software reliability, probabilistic models, statistical models, partial performance criteria, linear programming, vector optimization, decision theory

The article examines the two-dimensional flow around rectangular cylinders with an aspect ratio from 0.1 to 2.0 using the k-Realizable turbulence model with a Reynolds number of 2×E5. Numerical calculations in the ANSYS Fluent program have obtained changes in the coefficients of drag, transverse force and the Struhal number depending on the size of the prism section. The calculations were carried out at the intensity of turbulence of the incoming flow 2% and 4%. According to the results of calculations, it was found that with turbulence 4%, there is a good coincidence of the total aerodynamic characteristics with the available experimental data.

Keywords: flow around a rectangular cylinder, k-e Realizable turbulence model, aerodynamic characteristics of a rectangular cylinder

A two-dimensional coefficient inverse problem of thermal conductivity for a finite functionally graded cylinder is investigated. The thermal conductivity coefficient is considered to be variable along the radial and axial coordinates. The direct problem of finding the temperature distribution at different moments of time with known boundary conditions and the thermal conductivity coefficient is formulated in a weak statement and solved in the FreeFem++ finite element package. The influence of various two-dimensional power laws of the thermal conductivity coefficient on additional information (the temperature of the outer surface of the cylinder) is investigated. A projection-iteration scheme is constructed to solve the inverse problem. The thermal conductivity coefficient is presented as the sum of the initial approximation and the correction function specified as an expansion in a system of polynomials. At each stage of the iteration process, the expansion coefficients are calculated from the solution of the system of algebraic equations obtained by discretizing the operator equation of the first kind. The results of computational experiments on restoring various two-dimensional laws of change in the thermal conductivity coefficient are presented.

Keywords: functionally graded cylinder, finite element package FreeFem++, identification, thermal conductivity coefficient, inverse problem, iterative-projection approach, operator equation

The work is devoted to the development and research of a heat exchanger for a contact gas-liquid heat exchanger. To increase the efficiency of heat transfer, the surface receiving heat is equipped with longitudinal fins and transverse partitions that form vortex structures in a turbulent gas flow. The expected decrease in gas temperature is 300-600 °C when cooled with water at a temperature of 50 °C. Simulation modeling has been carried out, including analysis of temperature distribution and hydraulic resistance, thermal power and stresses.

Keywords: heat exchanger, efficiency improvement, exhaust flue gas, heat recovery, mixing heat exchanger, numerical modeling, mathematical model, pixelation method

The article discusses the developed software application for synchronizing the class schedule in the Modeus system with other systems and various devices. The experience of creating a service that integrates the class schedule into the calendar application, ensuring the relevance of data and its availability to users is described in detail. The features of interaction with the Modeus platform are analyzed, including disadvantages such as unstable access and the need for manual data entry. Mechanisms for optimizing the schedule update using the iCalendar format are proposed, which allows automating processes and reducing the likelihood of errors. The results of implementing the developed application, its impact on improving the convenience of the educational process for students and teachers are presented, and the prospects for scaling the application to other educational institutions are considered.

Keywords: curriculum, university, Modeus, SaaS, software agent, calendar, information board, iCalendar, BOOCO, educational process

The article considers the numerical solution of the dynamic problem of interaction of a a building with a foundation. The developed algorithm and computer program are implemented on the example of calculating a 9-story frame building taking into account the operation of bored piles from the impact in the from of a given earthquake accelerogram.

Keywords: numerical modeling, bedrock, accelerogram, spline approximation, bored piles, partial frequencies, integration step

The article is devoted to the development of a new mathematical method for modeling radial plain bearings having a polymer coating with an axial groove on the bearing surface. For the calculation evaluation of technical solutions for wear resistance, the compressibility of a truly viscous lubricant under laminar flow conditions is taken into account. As a result, new mathematical models were obtained that make it possible to estimate the duration of the hydrodynamic flow regime of the lubricant, to prove the stability and possibility of changing lubrication modes from boundary to hydrodynamic, as well as to make a calculated assessment of the effect of compressibility of the lubricant and wear resistance on operational characteristics.

Keywords: modeling, mathematical method development, modified design, compressibility impact assessment

With the development of scientific and technological progress, the use of modern data forecasting methods is becoming an increasingly necessary and important task in analyzing the economic activity of any enterprise, since business operations can generate a very large amount of data. This article is devoted to the study of methods for forecasting financial and trade indicators using neural networks for enterprises of the Krasnodar Territory. The indicators under consideration are the company's revenue for the reporting period, the number of published (available for sale) goods, as well as the number of ordered goods during the day, week and month. In this study, a multilayer perceptron is considered in detail, which can be used in revenue forecasting tasks using neural networks, and neural network predictive models "MLP 21-8-1", "MLP 21-6-1", and "MLP 20-10-1" are built based on data from the online auto chemistry store Profline-23.

Keywords: automated neural networks, marketplaces, forecasting, neural network models, mathematical models, forecasting methods

The development of digital technologies stimulates widespread automation of processes in enterprises. This article discusses the problem of determining the values of the oil indicator of a transformer from the resulting image using computer vision. During the study, the device of the MS-1 and MS-2 oil indicators was studied and the features that must be taken into account when recognizing the device in the image and determining its value were considered. Based on the processed material, a method for recognizing device elements in an image has been developed using the OpenCV library and the Python programming language. The developed method determines instrument readings at different angles of rotation and in different weather conditions, which confirms the effectiveness of the proposed method.

Keywords: technical vision, oil indicator, contour recognition, OpenCV library

The paper describes a multifactorial nonlinear regression model of revenue dynamics of the mining and metallurgical company Severstal, based on retrospective information for 2009-2021. Production volumes by type were used as independent variables: hot-rolled and cold-rolled sheet, galvanized sheet and sheet with other metal coating, rolled products, large diameter pipes, other pipe products and profiles. The criteria of multiple definition and Fisher, as well as the average absolute approximation error, were used as criteria for the adequacy of the model. A model competition was held to select the best regression dependence. As a result, a model is constructed containing inverse transformations of two independent variables in the right part.

Keywords: regression model, least squares method, adequacy criteria, mining and metallurgical company, revenue, model competition

This work is devoted to the study of the possibility of determining heart diseases on the basis of 13 categorical and numerical signs. We present a detailed analysis of the dataset, including dividing the data into training and test samples, dividing features into numerical and categorical, applying 4 different classification algorithms, checking the quality of the model using two techniques – delayed sampling and cross-validation. To assess the quality of the model, we pay attention to the value of the recall metric and the error matrix built on the test dataset from the deferred sample or on each test fold when using cross-validation. The results of the study are important both for a deep understanding of the relationship between certain medical indicators and heart disease, and for the development of effective methods for predicting them in the presence of individual symptoms.

Keywords: cardiovascular diseases, classification task, quality metrics, cross-validation, recall, machine learning, random forest

One of the most important points in increasing the conversion component of a web resource is identifying the most attractive places for the site user. To identify these locations, a site user activity data visualization tool was created that provides a visual representation of each user action on a site page.

Keywords: heat map, site, oculograph, fixation, priority area

Overhead power line wires are affected by various external factors such as wind, ice deposits, variable temperature conditions, excessive humidity. This eventually leads to fatigue failure of the wire. It consists in the origin and slow growth of a fatigue crack. The final stage of destruction is the sudden movement of the crack at high speed. The paper proposes a model of slow crack growth, at the mouth of which there is a grain boundary. Under the influence of external stress, a section of the border is a source of vacancies. The resulting vacancy concentration gradient between the grain boundary and the free surface at the crack mouth leads to a diffusion flow of vacancies into the crack. From the solution of the diffusion problem, the magnitude of the flow and the rate of increase in the crack length are found.

Keywords: crack, grain boundary, vacancy diffusion, fatigue failure, air line, mechanical stress, vacancy flow

The article considers a variant of constructing a digital twin model for diagnostics of operation of a mechanical gear transmission - a reducer consisting of a pair of cylindrical gears. The basis of the considered digital twin model is an adaptive learning vibration mathematical model of the static operating mode when gears rotate at a constant speed. The vibration signals of the reducer, recorded by accelerometers and effective for detecting and diagnosing faults, are used as the main information measured at the facility. The detected faults are cracking, wear, chipping and pitting of teeth. A special feature of the implemented digital twin is the ability to simultaneously detect faults of several teeth at once, both on the driving and driven gears, by time and frequency characteristics, as well as the ability to determine the main technical data of a specific reducer by vibration characteristics.

Keywords: diagnostic mathematical model, digital twin, vibration diagnostics, mechanical gearbox, tooth defect, diagnostic signal, vibration power spectrum, synchronously averaged time characteristic