Construction Of Mathematical Model Research Articles

Mathematical Model of an Antenna-Waveguide Path with Separation of Signals by Frequency–Polarization

Introduction. The creation of antenna-waveguide paths of multi-band mirror antennas (AWP MMA) is a significant task in the development of antenna-feeder devices for satellite communication systems (SSS). This task involves the construction of an adequate mathematical model of AWP MMA both without and with the implementation of an auto-tracking function built using the "frequency separation – polarization separation" method. However, the existing mathematical models have been developed only for specific AWP MMA types, thus making them unsuitable for the development of new AWP MMA. The model proposed in this paper can be used for an arbitrary number of combined frequency ranges and types of polarization.Aim. Development of a mathematical model of the AWP MMA of SSS both without and with the implementation of an auto-tracking function built using the "frequency separation – polarization separation" method.Materials and methods. The mathematical model under consideration assumes a description of the AWP MMA using block matrices. Each of these matrices describes the complex amplitudes of signals arising in each of the AWP MMA devices. This, in turn, makes it possible to analyze the influence of the parameters of each device on the characteristics of the AWP MMA of SSS as a whole with an arbitrary number of combined frequency ranges and types of polarization.Results. Two options for the construction of AWP MMA of SSS are proposed. The first option can be used in communication system antennas with software support, while the second option is applicable when a monopulse tracking method is implemented. To construct an AWP MMA model, it is proposed to use a matrix description of the characteristics of AWP MMA devices. This allows the structure of the considered AWP MMA to be varied within a wide range.Conclusion. The developed mathematical model makes it possible to describe the characteristics of each of the devices in the AWP MMA system using a certain multipole. The proposed model provides ample opportunities for controlling, at the stages of development, production and debugging, not only the characteristics of each device in the AWP MMA, but also the transmission coefficient and polarization isolation in each frequency range of the entire AWP MMA. The presented dependencies can be used to assess the relationship between parameter tolerances and the limits of changes in the characteristics of the motor vehicle.

System analysis of mathematical models of placement of transport and logistics facilities of different levels

Introduction. The formation of an overarching network of nodal freight multimodal transport and logistics centres in the Russian Federation and organisation of high-speed freight traffic on schedule on its basis requires the development of science-based proposals for the creation or modernisation of the corresponding regional transport and logistics infrastructure. One of the most important tasks in the implementation of this project in the context of limited investment resources is the correct justification of the number and choice of locations for the transport and logistics centres of the overarching network in the Russian Federation, as well as the locations of transport and logistics centres in the constituent entities of the Russian Federation.Materials and methods. This article provides an evaluation analysis of the classical methods for finding optimal centres on a plane and some construction of mathematical quantitative models for the optimal placement of transport and logistics facilities.Results. According to the evaluation analysis, the authors have drafted a scientifically based concept of a systematic approach to the issues of rational design and placement of elements of transport and logistics infrastructure, in particular, the overarching network of nodal freight multimodal transport and logistics centres, as part of a new highly efficient transport and logistics infrastructure of the Russian Federation and its international transport corridors.Discussion and conclusion. The obtained results of the study can be used for scientifically based decision-making in investment projects related to the development of transport and logistics infrastructure at both regional and federal levels: substantiation of locations and technological capacities of transport and logistics infrastructure facilities; determining the need for the development of objects of the regional transport and logistics infrastructure, while eliminating their bottlenecks; implementation of a phased set of measures to modernise the existing terminal and logistics complex.

Construction of Mathematical Model of Logistics Delivering Based on Intelligent Mobilization

Distribution process is the core of logistics enterprise system. Efficient distribution process is the key for enterprises to improve logistics service level, gain competitive advantage, and win customers. In order to reduce the design error of the system and ensure the effective operation of the system, this paper establishes the system model and analyzes the properties of the model through the evaluation and analysis of various resources of the distribution system. The future development of intelligent logistics system is not only the key for logistics enterprises to win competition, but also a new measure to promote China’s economic development. This is not only a typical NP hard problem, but also a major challenge for the rational and scientific development of the intelligent logistics industry. Based on the previous theoretical research results, this paper intends to explore the intelligent logistics distribution route selection scheme by using mathematical modeling methods such as particle swarm optimization, so as to provide new technologies and methods for logistics distribution operation and management decision-making. The results show that compared with the traditional genetic algorithm, the accuracy of the improved particle swarm optimization algorithm is improved by 10.36%. This method effectively improves the operation cycle and link efficiency and achieves the purpose of optimization. The improved particle swarm optimization algorithm proposed in this paper is not only more suitable and effective for enterprise decision makers to deal with subjective judgments in an imprecise environment. It is also based on the evaluation sequence of each indicator of the alternative obtained from the evaluation and the comprehensive evaluation of all indicators. By weighting and considering the results, the best solution for enterprise logistics and distribution is selected.

Modeling and Optimization of Triple Diode Model of Dye-Sensitized Solar Panel Using Heterogeneous Marine Predators Algorithm

The reliable mathematical model construction of dye-sensitized solar cells (DSSCs) using the triple-diode model (TDM) is proposed but it is a challenge due to its complexity. This work implements a novel method incorporating a recent meta-heuristic optimizer called the heterogeneous marine predators algorithm (H-MPA) to identify the nine parameters of the triple-diode equivalent circuit of DSSCs. In the optimization procedure, the nine unknown parameters of TDM are employed as decision variables, but the objective function to be minimized is the root mean square error (RMSE) between the experimental data and the estimated data. To prove the superiority of the H-MPA, the obtained results are compared with the slime mold algorithm (SMA), Transient search optimizer (TSO), Manta-Ray Foraging Optimization algorithm (MRFO), Forensic-Based Investigation (FBI), Equilibrium optimizer (EO), and Artificial ecosystem-based optimizer. The primary findings demonstrated the superiority of the proposed strategy in building a consistent model of the triple-diode model of DSSCs.

МАТЕМАТИЧНІ МОДЕЛІ СИСТЕМИ ТЕХНІЧНОГО ОБСЛУГОВУВАННЯ, МОДЕЛІ СТАНІВ У СФЕРІ ОБСЛУГОВУВАННЯ ОЗБРОЄННЯ ТА ВІЙСЬКОВОЇ ТЕХНІКИ

An analysis of the state of the system for the use and restoration of the technical condition of weapons and military equipment (WME) indicates an imperfectly moderate and, accordingly, inefficiently calculated planned restoration using the forces and means of restoring weapons and military equipment. Thus, the imperfectly thought-out system for processing data on the provision of spare parts for equipment is not provided for in a timely manner and is not always accurately and reliably calculated by persons directly responsible for the technical condition of combat vehicles assigned to them. On the basis of operational data, it is necessary to assess the degree of operational readiness of weapons and military equipment when applying the system of maintenance measures recommended in the operating instructions for weapons and military equipment samples. The construction of mathematical models is a preventive measure for carrying out computational processes for the operation of weapons and military equipment and, as a result, understanding the critical points in operation through the consideration of models of weapons and military equipment states in a planned preventive system, the implementation of a qualitative distribution of weapons and military equipment flows by type of state, failure, which accompanies the operation of combat vehicles of training units, which employs personnel practically unfamiliar with the procedure and correctness of safe operation. The study by simulation methods allows you to trace the impact on the frequency of maintenance and the level of operational readiness of the WME sample. Keywords: mathematical model, state models, simulation modeling, flow distribution, failure, maintenance, operation of combat vehicles, technical condition, restoration.

Mathematical Model Construction of Teaching Evaluation in Colleges and Universities Based on Convolutional Neural Network under the Background of Big Data

With the development of teacher evaluation, the main purposes of university evaluation are divided into the final purpose of ensuring teaching quality and the formative purpose of promoting professional learning. In order to effectively help teachers teach students according to their aptitude and realize personalized learning. This paper mainly analyzes and studies the mathematical model of college teaching evaluation based on convolutional neural network under the background of big data. The research analyzes the teaching evaluation under the background of big data and evaluates the teaching of big data participants. The teaching evaluation data can promote the development of education and teaching. Data acquisition processes and functions in the context of big data. Ensure the comprehensiveness and accuracy of data collection. At the same time, the function of teaching evaluation results is analyzed. The evaluation and formulation of mathematical model program in this study make full use of education big data information to provide scientific support for education decision-making.

Proposal for Teaching Mathematical Modelling Using COVID-19 as an Example of an Infectious Disease Epidemic: The Case of Japan in the Corona Vortex

Someone with a mathematical background can understand that if a virus such as COVID-19 enters a country, it will increase exponentially and cause a pandemic. Are students watching daily news reports with this level of sensibility? It is not difficult for students already familiar with differential and integral calculus to use the susceptible-infected-recovered or removed model to predict the number of new infections and determine the effect of self-restraint. Current education practices emphasize the memorization of concepts. When confronted with unknown difficulties such as COVID-19, it is important to develop teaching materials that, rather than frightening and emotionally discouraging students, enable them to utilize their previous knowledge, confront the difficulties, and explore the significance of mathematics education. This study provides example mathematical modelling material. Students learned mathematical modelling using the example of the number of new infections in Japan’s first wave of COVID-19. A survey was conducted before and after instruction which revealed that students in Japan are not being taught how to build mathematical models, and teaching using mathematical models can be used successfully to help students learn construction of mathematical disease models and also about exponential change.

Mathematical model and genomics construction of developmental biology patterns using digital image technology.

Biological pattern formation ensures that tissues and organs develop in the correct place and orientation within the body. A great deal has been learned about cell and tissue staining techniques, and today’s microscopes can capture digital images. A light microscope is an essential tool in biology and medicine. Analyzing the generated images will involve the creation of unique analytical techniques. Digital images of the material before and after deformation can be compared to assess how much strain and displacement the material responds. Furthermore, this article proposes Development Biology Patterns using Digital Image Technology (DBP-DIT) to cell image data in 2D, 3D, and time sequences. Engineered materials with high stiffness may now be characterized via digital image correlation. The proposed method of analyzing the mechanical characteristics of skin under various situations, such as one direction of stress and temperatures in the hundreds of degrees Celsius, is achievable using digital image correlation. A DBP-DIT approach to biological tissue modeling is based on digital image correlation (DIC) measurements to forecast the displacement field under unknown loading scenarios without presupposing a particular constitutive model form or owning knowledge of the material microstructure. A data-driven approach to modeling biological materials can be more successful than classical constitutive modeling if adequate data coverage and advice from partial physics constraints are available. The proposed procedures include a wide range of biological objectives, experimental designs, and laboratory preferences. The experimental results show that the proposed DBP-DIT achieves a high accuracy ratio of 99,3%, a sensitivity ratio of 98.7%, a specificity ratio of 98.6%, a probability index of 97.8%, a balanced classification ratio of 97.5%, and a low error rate of 38.6%.

Determination of the Optimal Algorithm for the Operation of a Hybrid Power System with a Regulating Generator

The purpose of the article is to study the possibilities of preventing the imbalance caused by the stochastic nature of RES by regulating the electricity accumulation and the backup generator. The subject of the research is random processes of energy generation and consumption. The goal is achieved by a mathematical model construction in which the system parameters would be formalized and allow the choice of optimal options. The mathematical model uses random functions to obtain statistical estimates, and is implemented as sequential models of energy generation and consumption as an integrated random process. The models’ adequacy is confirmed by comparing the simulated and real indicators for a number of existing RES in Ukraine. The proposed approach made it possible to establish the presence of system parameters that minimize energy losses and consumption, reduce the probability of energy imbalance, and effectively use the reserve power. The proposed mathematical model allows determining the probability of various system states, it estimates the reliability of energy supply, and minimizes losses at the stages of designing a power system and planning its operating modes. The above estimates are typical for certain climatic conditions and modes of energy consumption, and are of a specific nature. The significance of the work lies in the fact that the proposed formulation of the problem makes it possible to adapt the mathematical model to various conditions, to find implicit dependencies between the technical parameters of the system and its indicators in order to find optimal solutions.

Variational approach to the construction of discrete mathematical model of the pendulum motion with vibrating suspension with friction

The main purpose of this work is, first, a construction of the indirect Hamilton’s variational principle for the problem of motion of a pendulum with a vibration suspension with friction, oscillating along a straight line making a small angle with the vertical line. Second, the construction on its basis of the difference scheme. Third, to carry out its investigation by methods of numerical analysis. Methods. The problem of motion of the indicated pendulum is considering as a particular case of the given boundary problem for a nonlinear second order differential equations. For the solution of problem of its variational formulation there is used the criterion of potentiality of operators — the symmetry of the Gateaux derivative of nonlinear ˆ operator of the given problem. This criterion is also used for the construction of variational multiplier and the corresponding Hamilton’s variational principle. On its basis there is constructed and investigated a discrete analog of the given boundary problem and a problem of motion of the pendulum. Results. It is proved that the operator of the given boundary problem is not potential with respect to the classical bilinear form. There is found a variational multiplier and constructed the corresponding indirect Hamilton’s variational principle. On its basis there is obtained a discrete analog of the given boundary problem and its solution is found. As particular cases one can deduce from that the corresponding results for the problem of motion of the pendulum. There are performed numerical experiments, establishing the dependence of solutions of the problem of motion of the pendulum on the change of parameters. Conclusion. There is worked out a variational approach to the construction of two difference schemes for the problem of a pendulum with a suspension with friction, oscillating along a straight line making a small angle with the vertical line. There are presented results of numerical simulation under different parameters of the problem. Numerical results show that under sufficiently small amplitude and sufficiently big frequency of the oscillations of the point of suspension the pendulum realizes a periodical motion.

Intelligent meta-model construction and global stochastic sensitivity analysis based on PSO-CNN

A large-scale simulation model is needed for the stochastic sensitivity analysis of structural uncertainty. The finite element method often exceeds the computing power and cannot meet the analysis requirements and computational efficiency of stochastic sensitivity analysis. With the development of artificial intelligence, the calculation efficiency problem can be solved by a combination of the finite element model and a mathematical model, but the accuracy of the analysis results depends on the accuracy of the mathematical model. However, using artificial neural networks to construct mathematical models also has numerous problems, such as falling into local extrema. Thus, to address the computational efficiency and calculation accuracy problems, the particle swarm optimization (PSO)-convolutional neural network (CNN) meta-model is presented in this paper. This model was used to improve the training and prediction accuracy of a small-sample CNN, where the initial learning rate of the CNN was optimized by PSO. Additionally, the PSO was combined with the Adam optimizer to automatically screen the optimal network structure. The global stochastic sensitivity analysis method based on the Sobol sensitivity method and the Monte Carlo method was used to quantify the degree of influence of the input parameters on the model output parameters and to analyze the influence trend of the parameter changes on the structural response combined with the positive and negative Spearman’s rank correlation coefficients. The accuracy, good adaptability, and extension ability of the PSO-CNN meta-model was verified using the high-dimensional function examples and the structural models. Global stochastic sensitivity analysis was carried out on the joint of an extended end plate. The influence degree of the parameters on the initial rotational stiffness of the joint was determined, and corresponding design suggestions were obtained. These suggestions were consistent with the design specifications and the research results of other scholars, which verified the reliability of this method and could be applied to other types of structural sensitivity analyses.

Importance of careful data tracking for short-term prediction of COVID-19 case and death numbers from official resources

During the COVID-19 outbreak, governments, scientists, health workers, and numerous people worked on strategies or solutions for halting disease propagation. Unfortunately, the need for monitoring is steeply increasing, and taking necessary and restrictive actions is currently unavoidable. Due to the lack of epidemiological data and constantly changing numbers, constructing less error-prone predictive models and reliable mathematical models for the near future will help make better legal actions and prevention strategies. 
 In this study, daily data of eleven countries between 01/21/2020-05/02/2020 and 01/21/2020-06/17/2020 were used to forecast the number of future COVID-19 events by using different forecasting models. Best fit models were chosen after analysis of present numbers with Auto-Regressive Integrated Moving Average(ARIMA), Brown’s LES, and Holt’s LES models based on MAPE values. 
 The study showed the least error-prone best-fit models for short-term future predictions by analyzing two datasets and demonstrated that models changed after data updates among the selected countries. Investigation of the data of USA (Holt’s MAPE=7,7 to ARIMA(2,2,0) MAPE=4,8 for case numbers and ARIMA (2,0,0) MAPE=5,7 to ARIMA(1,2,0) MAPE=3,4 for death numbers), Turkey (ARIMA(2,0,0) MAPE=4,0 to Brown's LES MAPE=1,7 for case numbers and ARIMA(2,1,1) MAPE=0,9 to ARIMA(0,2,0) MAPE=0,9 death numbers), Brazil (Holt's MAPE=6,2 to ARIMA(1,0,1) MAPE=36,4 for case numbers and Brown's MAPE=3,2 to ARIMA(1,2,0) MAPE=2,8 for death numbers), Russia (ARIMA(1,2,0) MAPE=6,8 to ARIMA(1,2,0) MAPE=3,5 for case numbers and ARIMA(1,1,1) MAPE=3,7 to ARIMA(2,2,0) MAPE=3,5 for death numbers) demonstrated that at the same time flow, updating data caused alterations in the model selection, which results with changes in the predictions.
 The results of this study indicate that using more than one statistical model has superiority in the current approaches and fluctuations in the numbers should be taken into account when using the data to construct mathematical models and create future predictions for the management of already complicated and exhausting COVID-19 pandemic. Thus, policies and restrictions against COVID-19 spread might be more successful after considering that adjusted predictions for providing more accurate results.

Synthesis of Algorithms for Compensating Systematic Errors Based on the Construction of Polynomial Mathematical Models of Radar Measurements

Synthesis of Algorithms for Compensating Systematic Errors Based on the Construction of Polynomial Mathematical Models of Radar Measurements

Construction of Mathematical Model of Enterprise Marketing Economic Analysis Based on Neutral Analytic Hierarchy Process

With the gradual opening of the market, the overall development of Chinese enterprises is “rapid development, gradual improvement of industry status, and promising prospects.” Not only the development of Chinese local enterprises is getting better and better, but also a large number of foreign-funded enterprises are pouring into the domestic market, and the competition pressure on domestic enterprises is increasing. The purpose of this study is to study the effect of neutral AHP on the establishment of the mathematical model of enterprise marketing economic analysis and to use the method of structural judgment matrix and hierarchical structural model to put forward a concrete practical analysis of enterprise marketing cost and business performance. The experimental results of this study show that the establishment of an enterprise marketing economic mathematical model based on AHP can help group companies maintain an annual revenue growth rate of more than 5.8%, while the annual revenue economic growth rate is less than 5% for companies that establish a mathematical model.

A bridging study analyzing mathematical model construction through a quantities-oriented lens

A bridging study analyzing mathematical model construction through a quantities-oriented lens

Construction of geological and mathematical models for modeling the oil pool of the Kenkiyak deposit

Geological and mathematical models of the oil reservoir of the post-salt Kenkiyak field have been investigated and built. 6 types of geological models have been proposed, and on the basis of these models, mathematical models of oil deposits have been developed. Geological models are built on the basis of research results, taking into account the requirements of regulating the development of the Kenkiyak field, the geological characteristics of the field and the rate of operation. The mathematical model is based on the basic Darcy equations and includes equations for conservation of mass and energy, equations for limiting mass and oil saturation. The issues of modeling and determination of the relative permeability at the end point are studied, the results of determining the parameters of the relative permeability of different formations at normal and high temperatures are presented. The results of identification of parameters of mathematical models are considered.

Calculation of storm fuel supply of a seagoing vessel: solving professionally-oriented tasks using cloud services

The information and communicative competency today is an integral part of professional training in any sphere. Due to the fact that nowadays big amount of work is done or monitored in the remote mode the requirement is stipulated for every specialist to be able to use digital technologies professionally. For a future seafarer it means, first of all, the ability to use modern technologies as the information and data resource and also it presupposes the ability to work with software libraries, to create data bases, to perform necessary calculations by means of cloud services inclusive. This component is of extreme practical importance as it enables the satisfaction of the social mandate to prepare future seafarers for the living in the information environment. The task is quite challenging so it requires the adequate knowledge level. That is why the main objective of the course “Information technologies” together with other subjects within the curriculum for the professional training in maritime academy is to develop the reliable scientific and methodological grounds for the realization of any professionally related tasks of future merchant feet officers. Specially selected tasks acquaint cadets with information technology in terms of implementing the solution of applied professionally oriented tasks, such as navigating the course, determining the location of the vessel, calculating stocks for the trip, etc. Therefore, the obligatory elements of the tasks are: construction of mathematical (computer) models;analysis of possible solutions to the problem; of technological processes, taking into account all factors influencing the process and methods of decision-making;implementation of mathematical models of problems in spreadsheets. This article proposes a strategy for solving an applied problem using an information-modeling approach to the analysis and evaluation of the technological process, namely, the algorithm for calculating the required voyage and storm fuel reserves of a marine vessel. Both office spreadsheets and cloud services were used to implement the mathematical model for solving this problem. The use of “cloud computing” technologies in the training of seafarers is due to the fact that, firstly, while on board, the master or ship mechanic can perform some components of their work, especially joint projects, in modern services, and secondly, these technologies, supporting traditional forms of education, is a new stage in the development of education and a cost-effective, efficient and flexible way to meet the needs of students in acquiring new knowledge.

Economic-mathematical methods and models in management of economic activity of agricultural enterprises

The paper summarizes the most common mathematical methods used in the analysis, planning, organization, and management of economic activities of agricultural enterprises. It is determined that mathematical methods in combination with qualitative, logical methods of analysis contribute to the correct assessment of production efficiency or assessment of individual economic phenomena. It is a set of methods that turns analysis into truly scientific means of production management. It is proved that the most important universal method of research of economic activity of the enterprise is the method of modeling and construction of mathematical model of economic object. The study of economic processes in agricultural enterprises with the help of economic and mathematical modeling allows to assess the level of efficiency of the enterprise for the past period and to predict the effect of the implementation of certain management measures. Particular attention is paid to the principle of classification of economic and mathematical models on various grounds used in agricultural production during management decisions. The optimization models which make the widest group of models are considered and are intended for a choice of an optimum variant which will provide the maximum efficiency of the enterprise. Different approaches to the choice of basic parameters for building models to determine the resource potential are presented. It is revealed that during modeling it is necessary to follow the system approach, considering not only separate components and their interrelations, but also all system as a whole. It is advisable to use a system of models of parameters, characteristics, condition, and behavior in the external environment of interconnected economic processes, taking into account the complex structure of the organization, which will increase the adequacy and accuracy of results obtained in management decisions by managers of agricultural enterprises. It is established that economic-mathematical modeling allows to effectively solve specific economic problems and practical problems in the field of enterprise management in order to minimize the negative economic consequences.

Technological Machines Operation by Identification Method

In order to effectively organize the process of agricultural enterprises, it is reasonable to involve management tools to build optimal models of interaction of individual components of the production process. The most significant part concerning the technical and economic efficiency is the technological process. However, the harvesting and postharvesting process is of the highest priority. The current stage of the management paradigm development includes the attraction of mathematical modeling in the organizational process. The construction of mathematical models is necessary at the stage of planning, organization, control, and is aimed at choosing such parameters of the technological process that will ensure the highest economic efficiency. At the same time, the validation process of the optimal parameters of machines and equipment that separate the grain receiving is of the most importance. While solving this problem, it is necessary to consider various efficiency criteria, the main of which are “loss volumes” and “reduced costs”. The criteria for the efficiency of the technical equipment of postharvesting grain process are the permissible values of agrotechnical requirements that consider the time of safe storage of freshly harvested grain mass without pretreatment and grain shatter losses due to its overripe. It is necessary to consider the maximum allowable volumes of losses during the postharvesting technological process. In order to define the best organizational solutions the iteration principle is used until a solution that meets the restrictions on the reduced costs level is found. The mathematical modeling in technological processes is carried out with the involvement of regression models that allow predicting the qualitative indicators of the operation of the pre-cleaning machine. As a result, it is possible to choose such a mode of equipment operation that ensures the production of grain that meets the regulatory requirements for the quality of the resulting product. The novelty of this study lies in the development of optimal ways for combine harvesters functioning. The article presents the methodology and procedure of optimizing the technological process during the postharvesting process of grain. The characteristics received as a result of experiments allow us to organize the technological process in an agricultural enterprise in the most optimal way so that it is economically and technically efficient.

Method of Cylindrical Linear Induction Motor Equivalent Circuit Parameters Determination and Performance Calculation Algorithm

Cylindrical linear induction motors (LIM) are currently used in many industrial applications. Task of modeling of electrical machine is of great importance for optimization of processes of design and manufacture of engines with optimal technical characteristics. Traditional approach of construction of mathematical models of asynchronous machines based on classical theory of electrical machines, in comparison with methods of field theory and numerical methods, is much simpler. Structurally cylindrical LIM are distinguished by the absence of transverse edge effects, which contributes to the use of the methods of the classical theory of electrical machines for construction of their mathematical models. In this paper proposes an analytical method of calculation of parameters of equivalent circuit and operating characteristics of cylindrical LIM. In work engine was studied, movable part of which is made in the form of solid steel bar with a copper coating. Equivalent circuits of linear induction motors of various designs (one-sided, two-sided, cruciform, cylindrical) are considered, and assessment of the possibility of their application for research motor is made. Work of cylindrical LIM on industrial mechanisms is characterized by relatively small value of working stroke. For such engines, it is difficult to carry out standard tests, in particular idle stroke test, in order to obtain data for calculation of parameters of the equivalent circuit. The paper proposes a method of experimental determination of parameters of the equivalent circuit. Stator active resistance is measured at direct current, and stator reactance is measured using out-of-rotor method. The remaining parameters of equivalent circuit are calculated according to short circuit experience and engine work mode without load (is taken as an idle stroke experience). It is shown that exact G-shaped equivalent circuit, when calculation of parameters of which active and reactive components of correction factor and active resistance of magnetization branch are taken into account, provides acceptable accuracy in determination of values of equivalent circuit parameters. Algorithm of calculation of work characteristics of cylindrical LAM based on equivalent circuit data is presented. Comparison of calculated and experimental data showed satisfactory results, error is not more than 7%. A new model for decomposition of the total power losses, which includes four components is proposed. Each of the components of the proposed model has a certain physical meaning due to the nature of electromagnetic processes in a three-phase four-wire system. Definitions to describe each of the proposed components are formulated. It is shown that each of supplementary components of the total loss power is proportional to the minimum possible loss power and to the square of the RMS value of the power, which is caused by its occurrence in three-phase four-wire power supply system, and it is inversely proportional to the mean square of the net power loss. The synthesized Matlab-model for verification of the four-component structure of power losses showed a high degree of its adequacy. The proposed model allows us to rethink the description of power losses in three-phase AC circuits and can be used in specialized measuring instruments for electrical networks monitoring. Using the information obtained in the monitoring process, it is possible to plan technical measures to reduce losses of electrical energy in the power supply system, as well as to estimate the capital costs of these measures.