ISSN 1991-2927

## Section: "MATHEMATICAL MODELING"

 V.N. Kovalnogov, I.A.Khakhalev, E.V. Tsvetova, L.V. Khakhaleva
 Mathematical modeling and numerical study of atmospheric boundary layer near windfarms The article analyzes Russian and foreign sources relating to the interaction of wind turbines with the surface layers of the atmosphere. It specifies the main problems of mathematical modeling of the atmospheric boundary layer near the wind farms due to adverse meteorological conditions, in particular, constant zero crossings in the autumn-winter period, various precipitation, a wide time range, air parameters, terrain and other features. The authors analyze the evolution of mathematical models of turbulence to describe the boundary layer near wind turbines from earlier to rapidly developing and currently used. To achieve greater accuracy and naturalism, it is proposed to use high-performance efficient algorithms based on combining scales and physics of phenomena. The authors propose a mathematical model for studying the state of the atmospheric polydisperse boundary layer under conditions of the Ulyanovsk wind farm, taking into account the dispersed particles in the flow, surface curvature, pressure gradient and other influences. Mathematical modeling, model, boundary layer, turbulent flow, wind power, wind farm.
 2021_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V.N. Kliachkin, A.V. Alekseeva
 Optimization of parameters of generalized dispersion algorithm at statistical process control When monitoring a real production process using statistical methods, the question of early detection of violations arises. In most cases, several indicators are monitored simultaneously in the production process, and a change in the values of some indicators leads to a change in others. If there is a dependence of indicators for their monitoring, multivariate statistical control tools are used, in particular generalized variance chart. By varying the parameters of the chart, its efficiency can be significantly increased, this allows minimizing the time the process is in an unstable state.Applying the approach of A. Duncan, which he developed for Shewhart charts, a formula for the expectation of the duration of an unstable state of a process was obtained and a Python program was developed to minimize it.To test the set optimization problem, the calculation of the data of two process indicators is given and the optimal parameters of the generalized variance chart are obtained, at which the duration of the process in an unstable state is minimal. Scattering stability, generalized variance, duration of unstable process state, optimization task.
 2021_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A.V. Golubkov
 On algorithm for detecting changes in the object motion mode The article deals with the solution to the problem of determining the motion mode of an object along a complex trajectory. A hybrid stochastic model is used to describe a complex trajectory. The solution of the problem is based on the application of a sequential decision rule about the choice at an unknown time of the hypothesis about the current mode of motion, with a limited size of the bank of competing Kalman filters. An algorithm is constructed for calculating the average size of the Kalman filter bank in the case of M-possible motion modes. The algorithm is developed in a general form, therefore, it can be used not only for the four types of object motion models considered in this paper, but also for any linear discrete-time models with Gaussian noise presented by equations in the state space. The algorithm for a priori estimation of the average size of a bank of competing Kalman filters for M-possible modes of motion is implemented in MATLAB, the results of computer simulation are presented. Stochastic discrete linear systems, hybrid stochastic model, Kalman filter bank, sequential decision rule.
 2021_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V.V. Ovsiannikova
 The efficiency analysis of generalized variance algorithm under the trend of multidimensional scattering The generalized variance algorithm is used to control the multidimensional scattering of the process. The generalized variance is understood as the determinant of the covariance matrix of the process. The control efficiency is estimated by the average length of the series, that is the number of observations from the moment of violation of the process to the moment of detection of this violation. Both analytical and numerical methods can be used to estimate the average length of the series for different control types. One of the most common types of the process violation is an abrupt or gradual increase in its dispersion. The aim of the article is to estimate the average length of the series of the generalized dispersion map under the trend of multidimensional scattering. Multivariate statistical control, average series length, generalized variance, process scattering trend.
 2021_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 F.A. Alekseevna
 The generalized variance algorithm application in multidimensional statistical control of the process based on individual observations In practice, the use of instantaneous samples for statistical control of the process is often impossible due to technical conditions or is not economically feasible. In this case, the process is monitored by individual observations. To control the average level of a multiparametric process based on the Hotelling algorithm, appropriate methods have been developed, but when controlling multidimensional scattering based on the generalized variance algorithm, a number of problems arise. Various approaches to the estimation of the generalized variance are proposed in the article, and their comparative analysis is carried out. The practical application of the proposed algorithms is also considered. Generalized variance, individual observations, sliding range.
 2021_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A.K. Ivanov, A.L. Savkin, D.M. Iastrebov, S.S. Shumilov
 Decision-making based on the receptor-ligand interaction methods The article deals with the mathematical models of decision-making in the management organization systems. The models are based on the receptor-ligand interaction methods studied in the biokinetics. The article describes an interaction between initial data coming to the organization system and knowledge database generated on the basis of operation experience. The combination of matching pairs creates decisions for resolving problems and achieving the goals. The interaction may take one or more stages. For one stage the models were developed in the form of differential equations when the starting amount of data is not equal to the one in knowledge database. When the amounts are equal, the model is represented as Riccati equation in a special form solving by an indefinite coefficient. The article considers cases when information recourses of initial data and the ones of knowledge database are not uniquely defined. The similar models are developed for two stages of interaction. The article gives the examples of calculation of information recourses amount for a decision in case of different ratios of initial data/ knowledge database. Organization systems, decision-making, mathematical models, receptor-ligand interaction.
 2021_ 3

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.

 V.R. Krasheninnikov, I.E. Kuvaiskova, O.E. Malenova, A.I. Subbotin
 Pseudogradient algorithm for identification of doubly stochastic cylindrical image Nowadays image processing problems are becoming increasingly important due to development of the aerospace Earth monitoring systems, radio and sonar systems, medical devices for early diagnosis, etc. However, the most of the image processing works deals with images defined on rectangular two-dimensional grids or grids of higher dimension. In some practical situations images are set on a cylinder, for example images of pipeline sections, blood vessels, rotary parts, etc. The peculiarity of the domain for specifying such images requires its consideration in their models and processing algorithms. The article deals with autoregressive models of cylindrical images and gives some expressions of the correlation function depending on the autoregression parameters are given. To represent heterogeneous images with random heterogeneities, ‘doubly stochastic’ models are used in which one or more images control the parameters of resulted image. The spiral scan of a cylindrical image can be considered as a quasiperiodic process due to the correlation of image rows. The article proposes the pseudogradient algorithms for the modal identification. The statistical modeling proves these algorithms give good model identification. Cylindrical image, doubly stochastic model, pseudogradient algorithm, quasiperiodic process, identification.
 2021_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 S.I. Makarenko, I.E. Afonin, O.A. Kopichev, A.S. Mamonchikova
 The general lanchester model defining multilateral conflicts The analysed studies of combat simulation shows that the theory of dynamic systems, in particular the Lanchester model, is used for dynamic simulation of military conflicts. A large number of Lanchester models, each of which takes into account particular and specific factors, has already existed. However, these models examine a symmetric bilateral conflict. At the same time, in the Lanchester models class there are no models of multilateral conflicts. The purpose of the paper is to form the generalized Lanchester model of a multilateral conflict. The elements of scientific novelty of this model are to take into account different strategies of parties in a multilateral conflict and different conflict levels for the strategies. This model allows us to study the dynamics of resources changes of the conflict parties, to identify local wins and losses in the transition mode of the model, to draw conclusions about the global wins and losses of the parties, to form recommendations about choice of the parties’ strategies and the values of the parameters of their strategies for achieving a global win. The article outlines the ways for further research on the development of this generalized Lanchester model. Combat simulation, war simulation, Lanchester model, conflict dynamics, multilateral conflict, conflict simulation.
 2021_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A.V. Vertemiagin, V.G. Litvin, I.V. Litvin
 Performance evaluation of computing system and network objects at different levels of survivability The article discusses an approach to calculating the performance of objects exposed to adverse effects (AE), based on Markov models of queuing theory operating in a random environment. Three types of models of service queuing systems with an unlimited and a limited queue are investigated differing from each other in the message processing modes performed in the recovery process after AE: (1) incoming messages continue to be executed with a different performance compared to the normal mode; (2) in the process of recovery, incoming messages are accumulated, and processing is blocked; (3) in the process of restoration, no messages are received and no processing of messages already in the queue is carried out. The modes of operation of objects change as a result of random influences of the external environment (cyberattacks, influences of the external environment or object failures). The models are considered under the simplest assumptions about the distributions of the input flows of messages arriving at the object, their service time, the distributions of the time of occurrence of the AE and the recovery time of the object after that (Poisson flows and exponential time of the considered time intervals). The developed models make it possible to evaluate the design decisions taken from the performance point of view on the organization of message service for a given survivability under stationary assumptions. Numerical examples illustrate the use of models for assessing performance indicators and some indicators of survivability of the objects under study. Performance, survivability, queuing systems, variable operation, Markov models.
 2021_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 K.N. Laptev
 Automation of the maple system calculations for building the discrete models of the marine-vessel course autopilot The article deals with a script created in the Maple language that allows to check the properties of complete controllability and observability of a mathematical model for a ship’s course autopilot as well as to compute the matrix parameters of a discrete model for its subsequent use when building an adaptive discrete Kalman filter in order to identify the uncertainty parameters of the model. Course autopilot of a marine vessel, Maple system, discrete model.
 2021_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 S.A. Ageev, N.S. Ageeva, V.V. Karetnikov, A.A. Privalov
 Adaptive method and algorithm for rapid estimation of traffic parameters in high-speed corporate multiservice communication networks The article deals with an adaptive method developed and an algorithm that implements it for the rapid evaluation of traffic characteristics and parameters in high-speed corporate multiservice communication networks. This algorithm operates in real-time environment. High-speed corporate multiservice networks are characterized by high dynamics of changing their state, including changes in the characteristics of transmitted traffic. Under these conditions, the automated network management system should provide the required quality of communication services and services provided to users. Thus, the relevance of this study is determined by the need to implement network management processes in a mode close to real time, with a given quality in the conditions of dynamic priority of unknown changes in network characteristics. The basis of the proposed method is the concept of conditional non-linear Pareto - optimal filtering by V.S. Pugachev, which consists in the fact that traffic parameters are estimated in two stages. Firstly, the forecast of parameter values is estimated, and then their correction is made with the following observations of parameters. Traffic parameter forecasts are made in a small sliding window, and refinement of current traffic parameter estimates is implemented by pseudogradient procedures, the parameters of which are regulated by the method of fuzzy Takagi-Sugeno logical output. In this case, increments in pseudo-gradient procedures are calculated relative to the average value of previous estimates calculated in a small moving window as well. This method reduced the average relative error of estimating the intensity parameters of non-stationary network traffic by 1.4-1.9 times, and also reduced the size of the sliding window in which it is processed from 1.7 to 4.2 times. The proposed method and algorithm belong to the class of methods and algorithms which require a preliminary training. The average relative error in estimating traffic parameters does not exceed 7%, which is a sufficient value for the implementation of operational network management tasks. Pseudogradient algorithm, conditionally nonlinear Pareto-optimal filtering, fuzzy logical Takagi-Sugeno conclusion, fuzzy rule base, fuzzy knowledge base.
 2021_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A.K. Ivanov A.L.Savkin I.V. Chernyshev
 The mathematical models of information decisions in operations controls The article proves the relevance of developing decision-support systems that ensure an automation of intellectual activity of operation controls officers. It gives a brief review of scientific researches in terms of psychology of behavior, perception and thinking; and shows the viability of mathematical models for decision-making based on the analogue ones in other science and technology domains having a corresponding mathematical apparatus. The authors create the scheme of information decisions made by operation controls, which includes several stages of initial data conversion and gradient distribution of information resources in a one-dimensional space of structural units. The complex of mathematical models for information decision making for three stages of conversion and for various modes of initial data entry has been developed. The first model describes the gradient distribution of initial data in the form of a partial differential equation, while converting stages are given as an ordinary differential one. The second model includes the gradient distribution of initial data and subsequently converted data in the space of operating controls. It is represented as a partial differential system. The third and fourth models additionally incorporate convective terms of partial differential equations. The article gives the analytical solutions of all models and the estimated structures of information resources allocation. Decision-making, mathematical models, partial differential equations, ordinary differential equations.
 2021_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 N.A. Pchelin M.A.Y. Damdam A.S.A. Al-Mesri A.A. Brynza
 The paradigm of neural network decoding of non-binary redundant codes The use of noise-tolerant coding in modern communication systems remains the only means of increasing the efficient energy of such systems. This parameter tends to increase in conditions when the receiver of the communication system is able to correct errors of a large multiplicity. At the same time, the existing experience of using various methods for decoding the received data to achieve such a goal in the format of algebraic or iterative procedures does not give a noticeable effect and leads to a large time cost and an exponential increase in the complexity of implementing the decoder processor. The reason for this situation is the passive position of the receiver, which, when processing each code vector, remains a fixator of the picture that occurred in the communication channel and, in general, by compiling a system of linear equations and then solving it, tries to identify the error vector. Some exceptions are permutation decoding systems, which, by selecting and using reliable characters from the number received at the reception, simulate the operation of their transmitter and compare the received (almost error-free) result of such encoding with the received combination [1, 2]. With the growing influence of destructive factors, such methods are ineffective. A natural question arises: are modern solutions in neural network technologies capable of improving the characteristics of code vector recognition systems in order to obtain acceptable machine time costs in order to achieve an increase in the energy characteristics of communication systems. Neural networks, redundant codes, cluster, pattern recognition.
 2021_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 I.G. Tetenkin V.A. Sergeev
 The measurement of thermal parameters by changing frequency of embedded ring oscillator The article describes a brief analysis of linear thermal models of digital integrated circuits (DIC) and algorithms for determining the parameters of thermal equivalent circuits of DIC-based on transient thermal characteristics (TTC). It distinguishes the difficulties in implementing the algorithm for determining the thermal parameters of the DIC-based on the method of structure functions according to the JESD51-14 document and describes a new method for measuring the FPGA TTC by changing the frequency of a ring oscillator embedded in the FPGA logic elements. It also considers the hardware-software complex used for measuring the thermal parameters of FPGAs and proposes a simple algorithm for calculating the thermal parameters of FPGAs based on the analysis of the FPGA TTC using methods of numerical differentiation. The specified algorithm for calculating thermal parameters has been tested on the example of FPGA TTC EPM240T100C5 and Lattice M4A5-64/32. Digital integrated circuits, thermal circuit, thermal parameters, transient thermal characteristics, FPGA, measurement, calculating algorithm.
 2021_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 I.A. Martynova
 Methodological support for the dividing of factorial sets substitutions The substitution and permutation functions are the main functions of information cryptographic systems that provide diffusion and mixing of information. It is required to analyze these cryptographic primitives while creating new algorithms for data transformation using such functions. A new scale of notation has been proposed for performing such analysis. This is the factorial sets statistical series notation scale. This scale of notation helps to index the factorial sets statistical series elements and establish a one-to-one correspondence between the number and a specific type of substitution. The use of this system provides a way to find new characteristics and properties of substitutions. Since substitutions of the factorial sets form a cyclic group, the operation on elements of this group can be determined. In the general case, the operation used is a multiplication of substitutions, but this paper suggests another operation for group determination. The article presents a capability for dividing the factorial sets substitutions. Two methods for implementing the substitution division operations are proposed such as a method of successive transition and a method of group transition, which are implemented through non commutative operation of multiplying on inverted substitutions. Substitutions, factorial sets, multiplying, dividing.
 2021_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A.K. Khalaidzhi
 Research of the cetlin method of automatic arrhythmia detection by ecg signals from mit-bih This article presents and solves the problem of evaluating the quality of the Cetlin method, which classifies the sequence of RR-intervals by the recordings of ECG signals from MIT-BIH, which have labels on R-peaks. To solve this problem, author proposes new quality metrics and describes developed algorithms for calculating them in real time with taking into account segmentation errors. Author analyzes the influence of the accuracy of the segmentation procedure for extracting the positions of R-peaks from ECG signal on the proposed quality metrics. Paper compares the quality of the Cetlin method and other existing algorithms for arrhythmia detection that analyze the duration of RR-intervals in accordance with a set of rules in real time. Article reveals advantages and limitations of the method. Paper shows that the method successfully detects SVEB and VEB arrhythmias. but has inertia, that leads to false positives, and is immune to morphological abnormalities that do not change the duration of RR-intervals. Author analyzes the influence of parameters of the Cetlin method on its quality according to the proposed metrics. Paper describes the procedure for searching the best parameters configuration. In conclusion, author reveals that there is no the only configuration, that achieves the best quality for each signal from MIT-BIH. The Cetlin method, arrhythmia, ECG, RR-interval, quality metric, segmentation, R-peak, MIT-BIH, real-time mode.
 2021_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A.A. Gladkikh, A.D. Bakurova, A.V. Menovshchikov, Basem A.S. Said, S.V. Shakhtanov
 Fractal clustering of group codes in the system of galois field The permutation decoding (PD) of group systematic noise-immune codes is proved to be the most efficient method in using the redundant data entered to the code as against other methods of decoding digital data [1-5]. This opens up the opportunity of solving a complex computational problem of finding an equivalent code (EC), which is used to search for the error vector. The essence of this solution is that the computational procedure of real-time search for EC for each new combination of redundant code is replaced by a preliminary process of training the decoder to put in accordance with each new permutation of characters the generating matrix of EC parameters, which are recorded in the decoder’s memory card during training. Thus, such a memory card is called a cognitive card (CC). The article estimates the memory size of the CC, when using the block code (15,7,5), and shows the possibility of implementing a permutation decoder on basis of existing integrated circuits based on proven statements. For the first time, the apparatus of fractal partitioning of augmented binary Galois fields using the clustering of the common space of code vectors of a given code is used to prove the main statements. An efficient algorithm is presented to search for a set of invertible matrices of rearranged codes that do not provide an EC and for this reason should be primarily detected in the decoding procedure of the received code vectors. Permutation decoding, cognitive decoder map, fractal, cluster.
 2020_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V.R. Krasheninnikov, I.E. Kuvaiskova, O.E. Malenova, A.I. Subbotin
 The hypothesis test of covariation functions of quasiperiodic processes systems represented by cylindrical image models The generally accepted mathematical model of a wide variety of natural, technical, economic and other objects that exist in time are random processes, for example sea waves, wind, vibrations of engines and hydraulic units, biorhythms, etc. An object is usually described by several parameters, that is a system of random processes or time series. The processes occurring in many objects have a form close to periodic – quasiperiodic, namely there is a periodicity with an element of unpredictability, for example speech sounds, vibrations of various technical objects, daily temperature fluctuations, etc. In order to formulate the problems of processing the quasiperiodic process systems, their mathematical models are required. For this purpose, authors propose models in which the processes are presented in the form of spiral sweeps on autoregressive cylindrical images. A suitable set of parameter values for these models provides a given degree of quasiperiodicity of individual processes and the given covariance relationships between the processes of the system. A criterion is proposed for testing the hypotheses about the correspondence of the observed system of time series to their model of the described type. The authors provide the examples of the application of this criterion with an analysis of the sensitivity to deviations of the model parameters from the expected ones are given. Quasiperiodic process, covariance function, hypothesis tests, criterion, significance level, test power.
 2020_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A.N. Zolotov, V.N. Kovalnogov, R.V. Fedorov
 Software and information system for analyzing the thermal state of turbine machine blades Increased input parameters of the pressure and temperature of the working fluid in gas turbine installations result in the complex gasdynamic and temperature operation modes of the blade apparatus, but it is the principal tool for improving the energy efficiency of gas turbine installations in general. Applying the efficient methods of mathematical modeling and numerical study of gas-dynamic processes of a turbine machine may simplify this process and reduce financial costs. The article considers the main methods of increasing the energy efficiency of modern gas turbine machines are considered. One of the implementation ways is the use of software systems for calculating the thermal state of turbine machine blades. Numerical modeling, thermal protection, convective film cooling, software and information system, dispersed flow, gasdynamic temperature stratification.
 2020_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 I.A. Martynova
 Substitution characteristics of factorial sets and criteria for choosing the single substitutions The substitution and permutation function, which are presented in the article as elements of a number of factorial sets, are the key functions of cryptographic systems that provide diffusion and mixing of information. A new scale of notation is proposed while analyzing this problem. This is the notation scale of a number of factorial sets. This scale of notation helps to index the elements of a number of factorial sets and establish a one-to-one correspondence between the number and a specific type of substitution. This allows analyzing substitutions characteristics systematically. This paper presents the basic concepts of a number of the factorial sets. It is noted that the permutations of the factorial sets form symmetric permutation groups, and specific permutations (when raised to a power) form cyclic groups. The group axioms are fulfilled for the permutations of a number of factorial sets. Also, the definition domain, the group operation of multiplication, and identical and inverse substitutions are given for them. The number of independent cycles, decrement, inverse, parity and sign are common characteristics of the substitutions of a number of factorial sets. The criteria for choosing single substitutions with the best characteristics are proposed. Substitution, a number of factorial sets, a number of insensitive cycles, decrement, inverse.
 2020_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 The study of the stability of aeroelastic systems by linear approximation This paper proposes an approximate method of studying the stability of solutions of nonlinear differential equations with partial derivatives, describing the dynamics of one class of aeroelastic systems. Based on the Galerkin (Krylov-Kantorovich) method, when presenting the desired deformations in the form (formula), the study of problems for differential equations with partial derivatives for w(x,t) reduces to the study of problems for nonlinear systems of ordinary differential equations for functions (formula) . It is shown that the structure of these systems allows using the known stability theorems by linear approximation. Thus, the study of the dynamic stability of aeroelastic systems is reduced to the study of uniform problems combined by a common approach to solving them. As examples, vibration stability conditions of a pipeline with liquid flowing inside it and a plate streamlined by a supersonic gas flow are obtained. Pipeline, plate, deformation, dynamics, aerohydroelasticity, stability, nonlinear model, partial differential equations.
 2020_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 N.V. Dorofeev A.V. Grecheneva E.S. Pankina R.V. Romanov
 Simulation and bifurcation analysis of geotechnical system stability under vibration The automation of control processes for the stability of geotechnical systems is a great challenge involving the development of methods for multivariate analyzing and forecasting the stability with the subject to the nonlinearity of material stiffness parameters. The aim of the study is to improve the efficiency of automated control systems for geotechnical stability by developing an approach to detect negative changes in bifurcation diagrams of vibration displacement parameters of object structures. The authors present a mathematical model of the dynamic behavior of structural elements of an object as an elementary unit of a geotechnical system that describes a response to an external vibration action. An algorithm of bifurcation analysis is presented, which allows authors to determine the initial transition stage of the object structure to an unstable state by the acceleration values of forced oscillations exceeding the model parameters. A bifurcation diagram of stability changes in the structure of object at the displacement resulting from the load increase under vibration action has been constructed. This diagram, which type of codimension-one bifurcations is merging, enabled to determine the critical load values resulting in an unstable state transition of a system due to the influence of a combination of vibration factors. The efficiency evaluation of the proposed approach was carried out by the comparison with the results of construction stability calculations obtained by the use of the dynamic coefficient. The difference between the values of the maximum object displacement without loss of the stability under vibration action, obtained by the standard calculation method and using the developed model, is 32.5%, and it is significant in the theory of structure stability. When exogenous vibration noise is used as a source of a sounding signal, the application of the developed approach in automated control systems for geotechnical stability enable to change the permissible stability thresholds of objects being exploited depending on the level and combination of influencing factors. Geotechnical system, automated monitoring, stability, nonlinear dynamics model, vibration action, bifurcation diagram.
 2020_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A.V. Alekseeva
 Improving the efficiency of statistical control of hydro-unit vibrations Some techniques of statistical process control can be applied in investigating an object for likely defects. In this regard, the multidimensional scattering is monitored with the use of a generalized variance algorithm. At fixed time intervals samples of observations are recorded, according to which the values of the determinant of covariance matrix (the generalized variance) are calculated. The corresponding point, falling outside the borders of control chart, indicates the process failure. The test results based on vibration data obtained from the hydraulic unit at the Krasnopolianskaia Hydroelectric Power Station showed that the algorithm of the generalized variance has an insufficient quick response relating to both gradual and spasmodic changes in the scattering level. To make the monitoring process more efficient, the following techniques have been suggested. The first one detects defects by analyzing special kind structures on the generalized variance chart. The second technique applies the warning borders on the chart and the third one implies an algorithm of exponentially weighted moving averages for generalized variance. All the tests revealed that the search for nonrandom structures on the generalized variance chart is most effective for the early detection of changes in the scattering process Generalized variance, average run length, hydraulic unit vibrations, warning borders, exponentially weighted moving averages.
 2020_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 O.M. Gorbacheva A.S. Borovskii
 Analysis of the mathematical model of the waste oil purification in a diesel locomotive engine The article analyses a mathematical model of the waste oil purification in the oil system of a diesel locomotive engine. Waste oil purification takes place directly in the engine during its operation, which enables to reduce considerably the time taken to purify, and to decrease the concentration of impurities in the oil. In the proposed system for automatic control of waste oil purification, the main monitored parameters are pressure and temperature of the oil being purified. During analyzing the analytical solution of the system, the authors studied an increase in the concentration of impurity particles, the behavior of particle velocities in the centrifuge, and determined assumptions, within the framework of which the velocity of impurity particles was simulated. The influence of the impurity particle shape in the oil was taken into account in making these assumptions. Centrifuge, parallel velocity component, perpendicular velocity component, monitored parameters, automatic system.
 2020_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V.A. Baboshin A.K. Chernykh M.G. Iashin K.N. Savinov
 Optimization elements in the plan of technical covering of objects in communication lines A method is proposed for solving the problem of distributing a limited integer resource of forces and means of transport support for technical cover facilities. The prospects of developing special mathematical software with the aim of improving the quality of management based on the automation of the processes of meaningful processing of information and decision support are justified. The novelty of the method is determined by the statement of the indicated problem in the form of an integer programming model. The method is characterized by the stability of the computational scheme to change the dimension of the problem, a small number of iterations and its rapid convergence to the optimal solution, which determines its effectiveness. Transport support, distribution, technical cover, algorithm for solving the distribution problem, mathematical methods, software.
 2020_ 3

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.

 E.I. Stepnova S.K. Kiselev
 Adaptation of displayed flight and navigation data in the aircraft electronic display system The problem of flight safety continues to be of great importance in civil aviation, despite today aviation is the safest mode of transport. Particular attention is paid to the human factor, since it has a significant impact on safety. The article analyzes the impact of eye strain caused by displayed flight navigation data on a pilot during landing and discusses how to reduce it. It considers how the pilot interacts with aircraft equipment. The flight data, increasing eye strain, but having no affects on successful landing of the aircraft is specified. The article substantiates the necessity of adaptive display of flight data on the screen during landing. The proposed adaptive method for displaying flight navigation data is supposed to reduce the pilot’s eye strain, which contributes to improved quality of piloting and ensures flight safety. Flight and navigation display, electronic display system, aircraft, display adaptation, pilot’s eye strain.
 2020_ 3

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.

 O.V. Zhiliaev V.N. Kovalnogov
 The analysis of a new physical method for measuring the fluid mass flow rate and density This paper gives the preliminary analysis of a new physical method of measuring the fluid’s mass flow rate and density which has been discovered by other authors. The need for exploration and development of the method is defined by its advantages in comparison with other currently existing systems for mass flow rate measuring such as Coriolis flowmeter. The new physical method under consideration is based on measuring the alternating pressure difference which would occur along the flow due to harmonic oscillations of the cross-section area of the pipeline which has flexible walls. It is shown that the new physical method gives the opportunity of simultaneous measurement of mass flow rate and liquid’s density. A mathematical model of the process of non-stationary flow of a liquid is built. The problem of non-stationary flow of a liquid is considered and solved as to be one-dimensioned one. The detailed and thorough derivation of the formulae of the mathematical model is performed. Some inaccuracies in formulae permitted by authors of the method are indicated at. The limitations in applicability of the method which had been indicated at by its authors are also essentially weaken. The theoretical examination and approval of conclusions about the applicability of the new method are made. Liquid, density, mass flow rate, pipeline, oscillations, measuring.
 2020_ 3

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.

 V. A. Baboshin B. Gavrilovich A. A. Iakovlev
 To the study of analysis on how harmonic radio interference affects the power supply systems of railway transport The railway transport is a complex organizational and technological system. Transit by rail freightage is contingent on many factors, including the traffic and carrying capacity of stations and track infrastructure. The efficient management of an operating station, as well as arrangement of safe rail traffic control affected by adverse factors is of crucial importance . One of such significant factors is the radio interference influencing electrical and electronic equipment, and equipment ensuring the automation of railway, remote control and telecommunications . The article discusses some issues of electromagnetic compatibility of the equipment, analyses how voltage variation in the overhead system affects the generation of harmonic radio interference for the equipment of power supply network, railway automation, telemechanics and telecommunications, when traction motors are running. This issue is essential to ensure the compliance with Eurostandards and concepts, regarding the compatible functionality of equipment, which influences the railway economics. The article emphasizes the compensating filters, which are put to practice use at traction substations of Serbian Railways as primary protection means . Railway transport, complex organizational and technological system, overhead system, distribution network, radio interference, harmonics, railway automation and telemechanics, telecommunications, economical efficiency, reliability.
 2020_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. N. Kovalnogov R. V. Fedorov A. V. Chukalin L. V. Khakhaleva
 Mathematical modeling of exchange processes in the turbulent boundary layer. Model analysis and verification The fundamental tool for studying complexgas-dynamic processes occurring under non-stationary conditions is mathematical modeling, which allows reliable studies to carry out comprehensive research and development of technical solutions. A promising area of research is the search and development of methods for controlling the boundary layer of gas flows, which can intensify or reduce exchange processes in the boundary layer of power plants used in various industries of our country, such as: energy, aircraft manufacturing, shipbuilding. A modern and effective control method is a method based on the use of a damping surface. The impact of the damping surface is expressed in a decrease in the intensity of generation of turbulent vortices, which in turn leads to an increase in the velocity in the boundary layer and a decrease in the friction and heat transfer resistance. Research and development of technology will allow developing technical solutions for efficient and resource-saving energy. The paper considers a method for modeling a turbulent boundary layer, which allows one to take into account the effect of the damping surface on the metabolic processes occurring in the boundary layer of the gas stream. The paper also presents the results of a comprehensive hot-wires anemometric study of the boundary layer of a gas stream on a damping surface. The experiment was carried out using certified equipment in a wind tunnel and aimed at developing the theory and verifying the software package, in which the simulation method is implemented. Mathematical modeling, numerical research, boundary layer, turbulence, laminarization, damping surface, heat and mass transfer.
 2020_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 I. A. Radionova A. L. Savkin
 Forecast modeling of peak work loads based on time series analysis The article deals with the analysis of work load in a technical documentation department of research-and-production association. Data for the analysis are formalized as unstructured time series (time series). Basic definitions of time series, methods for detecting anomalous data, trend criteria, trend equation types are studied. Methodology for data structuring of initial time series intended for the following analysis is developed. Modification of the criterion for anomalous point detection is proposed. All the considered algorithms are implemented; database structure is developed. Information on the department work performed during the period 2008 to 2018 was captured to carry out computing experiments. Data are structured according to the proposed methodology. Anomalous data are detected by standard and modified criteria; trend availability is identified. Conclusions are made on criteria and equations that are optimal for initial data set. Data for year 2018 are modelled based on various equations; results are compared with actual data. Conclusions were drawn up regarding the ability to be used the methods examined for the selected data set. Time series, trend, anomalous data, work load.
 2020_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

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