The paper provides a brief overview of publications on the application of mathematical modeling methods in the study of the patterns of functioning of hydroelectric power plants (HPPs). In particular, the following are considered: mathematical models of the total minimum water consumption for a cascade hydropower system in China; a mathematical model of hydropower plants; a mathematical model of two small hydroelectric power plants operating in tandem; accurate modeling of hydraulic transient characteristics in a complex drainage system. The task of filling in the gaps in the data concerning the operation of hydroelectric power plants is formulated. The approach to its solution is proposed to be based on the use of the method described in previous publications by one of the authors and based on the use of regression analysis apparatus. The specific task of filling in data gaps for a hydroelectric unit of one of the Siberian hydroelectric power plants has been solved. The following factors are used: active and reactive power of the electric generator, voltage, current and temperature of the stator iron, rotor current, air cooler hot air temperature.

Keywords: hydroelectric power plant, electric generator, data gaps, predictive analytics, regression model, adequacy criteria

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

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

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

3d-printing is the leading direction in world advanced technologies. For today 2614 patents were displaying in the Worldwide date base. General Electric is more effective companies in patenting materials for 3d-printing.

Keywords: materials for 3d-printing, review of patents

This article provides a description of the developed hardware and software complex for controlling lamps using the DALI protocol, design features and software code, recommendations for operation.and development of new production on available floor spaces. The most important organizational economic targets of a diversification of management are presented by innovative activity of the industrial enterprise.

Keywords: DALI protocol, lighting device, lighting control, Arduino, luminous flux

The article discusses the development and evaluation of the design of a rotary-type mechanized parking system, the use of which will solve the problem of shortage of parking spaces in large cities. The paper presents the results of the research, a patent analysis was carried out, the composition of the mechanized parking system was determined and a rotor-type design was developed, an engineering analysis of the design was performed using the Autodesk Inventor software system. The calculation showed that the structure meets the requirements for strength characteristics.

Keywords: mechanized parking system, modeling, parking space, durability, static research

The article is dedicated to analyzing methods for processing experimental data in the field of improving manufacturing technologies, with a focus on the processing of titanium alloys. In the modern context of natural science experiments, characterized by large volumes of information, there is a need to apply mathematical methods and computational systems for effective data analysis. Research conducted at the Department of "High-Performance Processing Technologies" at MSTU "Stankin" aims to identify the optimal type of wear-resistant coating for cutting tools when processing titanium plates. Titanium, with its low thermal conductivity and high chemical reactivity, presents certain challenges during processing, necessitating a thorough investigation of the relationships between cutting conditions and process parameters. The article discusses existing problems related to the insufficient study of these relationships and proposes a solution for data storage and processing through the creation of a unified database. This will enhance the visualization and analysis of experimental results, thereby improving the efficiency of research and the quality of manufactured products. The results of this work may be beneficial for both scientific research and practical applications in industry.

Keywords: technological process research, cutting tool, cutting mode characteristics, systems analysis

The study is devoted to the development of models, algorithms and software for computer training complexes (CTC) for training developers of automated information systems (AIS). The process of automated control of students' knowledge and skills using CTC in studying the mathematical support of AIS (using fuzzy modeling as an example) is formalized based on IDEF0 diagrams, and the process of assessing exercise performance as one of the control components. The advantage of CTC is that the teacher does not need to develop individual exercise options, since CTC configures the structure and complexity of the exercise and then automatically generates a unique version of the exercise for each student undergoing knowledge testing on the topic being studied. The student's performance is checked automatically by comparing the mathematical models of the student's solution to the task and the reference solution generated in CTC based on the problem statement. Algorithms for assessing task performance in fuzzy modeling exercises have been developed. A prototype of CTC has been created in the form of a web system with personal accounts for the teacher and the student. The developed concept and algorithms for monitoring knowledge and skills in fuzzy modeling using the CTC can be adapted for various disciplines in the field of mathematical, software, information and other types of support for AIS.

Keywords: automated information systems, mathematical support, fuzzy modeling, computer training complex, e-learning, distance learning

The paper methodologically shows the identity of the mathematical problem of graph path searching with the technical problem of searching for various defects in software, in particular, bugs and undocumented features. The graph model of software functioning, which became the basis for the presented methodology, is briefly described. New research directions based on graph theory problems, which have not been previously used to search for defects in software, are stated.

Keywords: graph model, software, graph pathfinding, breadth-first search, meet-in-the-middle method, malicious software

An analysis of the life cycle of food products, the relationships between indicators of production, consumption, food losses, as well as the quality of life of the population will allow us to form a number of measures to reduce food losses and food waste. The paper sets the tasks of identifying the sources of food losses based on a statistical study of the level of losses in the regions of the Russian Federation and an analysis of the life cycle of a food product. The analysis of indicators of production and product losses is carried out on the example of potatoes, vegetables, fruits, meat, milk, eggs. The correlation analysis of indicators of production, consumption of products, and food losses showed that the greatest losses occur at the stages of production, processing, and sale in retail chains. Clustering of the regions of the Russian Federation according to indicators of food losses has been performed. Clusters with high production, consumption, and loss rates and with low production, consumption, and loss rates were formed for each type of food under study. A model of the life cycle of food products in BPMN 2.0 notation is constructed. The stages of the life cycle characterized by food losses have been identified. General recommendations on food loss management have been formed.

Keywords: food losses, food loss modeling, correlation analysis, cluster analysis, business process modeling

The concept of digitalization of the construction organization project (POS) is presented, which is based on its close connection with the construction schedule. The place of the POS in the digital model of the building at the project stage (PIM) is considered. based on its digitalization, taking into account the relationship between information modeling at the project stage (PIM). The main problems that may arise when implementing the digital version of the POS in the general information model at the project stage are identified.

Keywords: BIM, TIM, POS, digital model, calendar schedule, construction organization

The article is based on the results of a scientific study on modelling the operation of the system ‘foundation - ground mass’ of a special type of deep foundation - gantry piles in conditions of ground mass during the construction of the overpass of the M-12 ‘Vostok’ highway. Gantry inclined piles are designed to transfer more load to the foundation than traditional vertical piles. The purpose of this study is to select the angle of inclination of gantry piles for overpass support on the basis of mathematical modelling. The scientific novelty consists in the selection of the gantry pile foundation design for the support of a motorway overpass by mathematical modelling.

Keywords: gantry piles, deep foundation, overpass, modelling, finite element method, soil massif, stresses, deformations, stanchion, foundation-soil massif system