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

Gantry piles have been developed to transfer a large load to the load-bearing foundation when erecting critical structures due to the larger contact area of the piles with the ground compared to vertical piles. The design of gantry pile foundations is the most labour-intensive. The responsibility of making a mistake increases when designing this foundation under seismic conditions. This paper deals with the modelling of the performance of cargo piles under seismic loading conditions in the construction of foundations for bridge piers. The results obtained are part of a larger scientific study on the feasibility of using gantry piles in high-rise construction in earthquakes of 6 to 10 on the Richter scale.

Keywords: gantry piles, deep foundation, seismic effects, overpass, modelling, finite element method, soil mass, stresses, deformations, foundation-soil mass system

The article considers the solution of the urgent problem of calculating the size of the effective focal spot of a microfocus X-ray tube using computer modeling methods. The principle of operation of the calculation method used by the authors is to compare interference images obtained using tested microfocus X-ray tubes with simulated interference patterns formed using the developed software by numerically solving the wave equation. It should be noted that modeling a one-dimensional interference pattern using fast Fourier transform requires a significant amount of RAM and takes considerable time even when using modern computer equipment. The paper presents the results of modeling phase contrast profiles for two types of test objects – nylon fishing line and aluminum wire. The considered method for determining the size of the focal spot is characterized by good sensitivity and allows efficient and high-precision calculations for all types of microfocus X-ray tubes.

Keywords: computer modeling, X-ray tube, microfocus source, focal spot, non-destructive testing

In the work, based on the previously constructed multifactor dynamic regression model of water level in the Iya River (Eastern Siberia), the authors forecast this indicator for June 2023 in three options: pessimistic, optimistic and neutral (base). A comparison of the forecasting results with the actual value of the water level confirmed the high adequacy of the model and good prospects for its future successful use to solve a wide range of applied and practical problems.

Keywords: regression model, river water level, lag time, seasonal variable, forecast, adequacy, criteria

The article solves the problem of diabetes mellitus diagnostics. Diabetes mellitus is characterized by high prevalence and significant costs for treatment and prevention of complications. This disease worsens the quality of patient's life, limiting their daily activities and functioning.To solve it, it is proposed to construct and use a neuro-fuzzy model. To train the model, the search and preparation of initial data for analysis were performed. The data were obtained from the publicly available Kaggle source. The data for analysis was prepared on the basis of the analytical platform Deductor. From the prepared data set, training and testing samples were formed, used to construct the model. Comparison of the obtained results with the known results of other authors allowed us to conclude that the model is adequate and can be used in practice.

Keywords: neuro-fuzzy model, fuzzy neural network, diabetes mellitus, modeling, diagnostics, machine learning

Indentation is a universal and practical method for obtaining material characteristics, especially when it is impossible or difficult to expose the material to other measuring methods. Experimental data on the mechanical properties of various types of materials were obtained using the shock loading unit. A mathematical model based on the finite element method was used to verify the experimental results. The article considers the solution of the problem of classification of neural metals with different mechanical properties. As part of the work, an artificial neural network has been created that allows the distribution of materials into selected groups. It is determined that a significant advantage of using neural networks is the ability to process experimental data and identify complex nonlinear dependencies, which makes them in demand in tasks related to the study of material properties.

Keywords: impact indentation, neural network, task of classification, artificial intelligence, dynamic indentation, non-destructive testing.

This paper analyzes the performance of solving the classification problem using various open-source artificial intelligence and machine learning libraries in the field of marketing and customer relationship management; based on the results of experiments, the best library is selected for the purpose of introducing artificial intelligence into domestic CRM systems based on numerical performance indicators.

Keywords: artificial intelligence, machine learning, big data, classification, marketing, customer relationship management, import substitution, open source

Paper presents an algorithm for analyzing and controlling data and project quality in construction using building information modeling and extensible markup language. The authors, argue that project quality stems from data quality and information quality. The proposed algorithm integrates BIM with extensible markup language, converting data quality and project quality criteria from employer information requirements into an extensible markup language scheme to ensure compliance with established standards. Key criteria for data quality and project quality include classification, identity, hierarchy, information identity, coordination, level of development , association, redundancy, staging, and spatial orientation. The algorithm involves creating a test BIM model, to simulate employer information requirements violations, performing checks using a Model Checker, automation tool in Autodesk Revit, and ensuring all criteria are met. The process includes saving verification checks, combining them, and generating reports in comma separated values format for transparency and further analysis. The authors highlight the importance of applying the algorithm from the early stages of project discussions, involving all participants to ensure the accuracy of data quality and project quality schemes. This approach leverages both international and domestic standards for continuous monitoring and immediate decision-making support throughout the project lifecycle.

Keywords: extensible markup language, information technical requirements, employer information requirements, building information model, information quality, project quality, model checking

The article explores the problem of creating aircraft flight models in the Simulink environment. The reference systems in which transformations are carried out are considered. The equations of motion used in the simplest converters are given. The initial conditions for the equations are determined: the speed of the body, the angular orientation of the body's pitch position, the angle between the velocity vector and the body, the speed of rotation of the body, the initial position, the mass and inertia of the body, the source of gravity, the acceleration due to gravity, the curb and total mass of the body, speed of air flow, inertia of an empty and full body, flight trajectory, etc. An analysis of converters of aerodynamic forces and moments into the trajectory of motion as part of an aerospace package in the Simulink environment was carried out. Recommendations are given for their use for various modeling purposes. The results of modeling a simple converter with three degrees of freedom are presented.

Keywords: modeling, MatLab, Simulink, equations of motion, aerodynamic torque, flight path, coordinate transformations, reference system, degrees of freedom

In this paper, we present the implementation of a neural network approach to solving the problem of handwritten signature recognition. We analyzed the main approaches to handwritten signature recognition. We identified the features of using a handwritten signature as an identification method, including the variability of a handwritten signature and the possibility of forgery. We identified the relevance of using neural networks to solve the signature recognition problem. We developed a neural network model for recognizing handwritten signatures, presented its architecture containing convolutional and fully connected layers, and trained the neural network model based on handwritten signatures "Handwritten Signatures" containing 2263 signature samples. The accuracy of the developed model was 92% on the test sample. We developed a web application "Recognition of a static handwritten signature" based on the developed neural network model on the Amvera cloud hosting. The web application allows identifying users based on a handwritten signature sample.

Keywords: handwritten signature, neural networks, signature recognition, image processing, machine learning, web application, cloud hosting, identification, verification, artificial intelligence

In residential and public buildings, in-floor convectors are often used as heating devices. This study examines the operation of convectors in a swimming pool room. The results of numerical modeling of room microclimate parameters taking into account calculated heat loads and moisture emissions are presented. A comparative analysis of the operation of various heating and ventilation systems for a public swimming pool was carried out. The results of the study were obtained in the form of temperature distribution fields, movement speeds and relative air humidity. A conclusion is drawn about the effectiveness of using in-floor convectors in indoor public swimming pools.

Keywords: heating system, in-floor convector, moisture content, excess heat, excess moisture, air exchange, numerical modeling, room microclimate, SolidWorks, STAR-CCM+

Nowadays, numerical methods are widely used to realise complex calculations.Verification of the correctness of the numerical calculation results is a relevant task. The validity of the results can be confirmed by determining the stress-strain state by various methods. This paper presents the results of the calculation of thin isotropic ring spherical shells of constant thickness with half-shell angle in the range of (90-170) degrees by two numerical methods. The results of solving the system of differential equations of the general moment theory of shells with the use of the computer mathematics system (Maple 2017) and the finite element method (FEM) are discussed. The given examples show that the calculation results with the use of the selected finite element KE-44 coincide with an accuracy of 10-15 % for shells with a half-shell angle of 120 degrees. When the angle is increased to 170 degrees, the difference in function values becomes significant. The paper gives some examples of calculation of ring spherical shells under the action of one and three annular loads. The variation of axial and radial displacements, of meridional bending moment for shells with the ratio of radius of the curvature to shell thickness 25, 50, 100, 200 is shown. Plots of meridional bending moment and moment isopole are given.

Keywords: elastic, spherical shell, numerical method, computer mathematics system, finite element method.

A Simulink model of a lightweight aircraft is being studied as part of the Aerospace Blockset package, including a system model of the aircraft, an environmental model, a model of pilot influences, and a visualization block. The structure of the flight model is considered and models of the effects of the environment and wind are disclosed in detail, consisting of blocks of physical terrain features, wind models and an atmospheric model, a gravity model, each of which is set to an altitude. The Wind Shear Model block calculates the amount of wind shear as a function of altitude and measured speed wind. The Discrete Wind Gust Model block determines the resulting wind speed as a function of the distance traveled, the amplitude and length of the gust. The turbulence equations comply with the MIL-F-8785C specification, which describes turbulence as a random process determined by velocity spectra. Simulation results are presented that reflect changes in the trajectory of movement under various wind influences specified in the wind speed gradient block.

Keywords: modeling, airplane flight, Simulink, Aerospace Blockset, crosswind, turbulence, turbulence equations, gravity model, motion trajectory

The article discusses the use of simplex methods of experiment planning to determine the optimal composition of composite building materials. Composite building materials are multicomponent systems, so their properties depend on a large number of factors that are diverse in nature and influence. The use of orthogonal plans is not able to adequately describe experimental data with a wide range of varying factors. Therefore, the article proposes to use simplex-lattice Scheffe's plans. A complete third-order model was developed to determine the optimal composition of the filled cement composite, and a regression equation was written. The adequacy of the equation was confirmed at the control points of the plan using the Student's criterion. The proposed planning method can be used to optimize the composition of multicomponent systems.

Keywords: multicomponent system, optimization methods, composite building material, experiment planning, simplex plans, Scheffe's polynomial, regression equation

The paper presents an algorithm for modeling production and economic characteristics for obtaining crop products, with the help of which planning problems are solved using multi-level parametric programming methods under average and unfavorable operating conditions for commodity producers. Since time series of characteristics associated with the production of products can be described by trends to assess adverse events, an algorithm for their identification was used based on the construction of multi-level trends according to the idea of ​​​​the hierarchical structure of the time series. When using this algorithm, a sequence of local minima is formed from the original series, a trend is built, and levels located below this trend, called unfavorable events, are identified. The assessment of the probabilities of these events is determined by the distribution law, which describes a number of differences in actual data and trend values ​​of a sequence of local minima. In the absence of trends and considering series of characteristics in the form of random variables, statistical and physical criteria are applicable to identify unfavorable events. As such, it is proposed to use the average value of local minima. Of the adverse events received, the smallest of them are distinguished, which represent rare events. Based on the identified events and other characteristics, the problem of optimizing the production of agricultural products is formed, the solution of which allows us to obtain optimal production volumes in accordance with maximum incomes corresponding to the calculated probability of events. A comparative analysis of planning results under average conditions and taking into account unfavorable events shows the likely losses of commodity producers at the enterprise and municipal district level.

Keywords: parametric programming, trend, adverse event, production and economic characteristics, crop production, losses, risks

motion of the body are obtained, which can only be solved numerically. The equilibrium equations are solved and the basic stationary modes of body motion are obtained. The main result is the most gentle body planning mode. In the matlab computer mathematics system, a set of programs is written that searches for a numerical solution and outputs trajectories. The movement of the modes under consideration is modeled and the stability of the main modes is looked at using numerical calculations.

Keywords: body, planning mode, stability, geometric dimensions

In this paper, we present a study dedicated to implementing a neural network approach to face recognition. We conducted a comprehensive review of existing face recognition methods. We developed a neural network model, trained on the DigiFace-1M dataset. This paper details the architecture of our developed neural network model and the step-by-step training process. The model achieved an accuracy of 78% on the validation set and 92% on the training set. We also addressed the integration of our model into the Russian Amvera Cloud service. As a result, we created a web application that allows users to identify themselves using uploaded images of their faces. This research demonstrates the potential of neural networks for face recognition tasks and offers a practical solution for implementing such systems in various fields.

Keywords: face recognition, deep learning, neural networks, user identification, model architecture, model training, model integration, cloud services, security, biometric technologies

Numerical methods for calculating shells provide a wide range of solutions when varying various parameters. The object of this study is a mathematical model of thin isotropic elastic shells of revolution of constant thickness. The problem is solved from the position of moment theory.To determine the stress-strain-state of the shell, the solving system is obtained by transforming the basic systems of equations of rotational shells by moment theory and the variables separation. All SSS and load components are decomposed into Fourier series along the circumferentail coordinate. A programme in the Python programming language was written to verify the numerical solution by a computer mathematics system (CMS-Maple 17). Matplotlib library was used for plotting graphs. Examples of numerical calculation of ring spherical shells for the action of ring loads are given. The variants of action of one and two ring loads on shells with different conditions of support along the contours and different half shell angles are presented. The difference between the calculation results of the two methods for bending moment functions and displacement functions is tabulated. The highest value of the difference is 0.0015%. Plots of the variation of meridional bending moment under the action of two ring loads are presented. The variants of rigid pinching along the contours and hinged support are considered. Exsmples are given for shells with the ratio of radius of curvature to shell thickness equal o R/h = 25, 50, 150, 200. Considered of the half shell angles equal to 90, 100, 130 degrees.

Keywords: rotation shell, spherical, isotropic, elastic, computer mathematics system, Python programming language

The article presents a numerical simulation of energy separation (thermal stratification) in a Leontiev tube, conducted using STAR-CCM+ software. The study focuses on a comparative analysis of two different tube designs, each intended to create temperature differences in gas flows. The simulation revealed that the supersonic flow passing through the tube significantly increases in temperature at the outlet, while the subsonic flow, on the contrary, shows a noticeable decrease in temperature. Detailed profiles of gas velocity and temperature are provided for both designs, demonstrating the effectiveness of each Leontiev tube variant in creating distinct areas of gas with different temperatures without the need for additional external heat exchange. The results obtained are of practical significance for improving the efficiency of gas distribution stations, enabling more effective management of thermal flows and preventing the formation of gas hydrates, as well as for use in other technological processes where temperature separation in flows is required without external heating or cooling.

Keywords: Leontiev tube, numerical simulation, STAR-CCM+, thermal stratification, gas flow