ISSN 1991-2927

## Section: "MATHEMATICAL MODELING"

 A. Ivanov, V. Tipikin
 Modeling Mutual Influence Of Information Flows The article deals with a subset of data flows that build an information space for bodies of state authority and administration. A subset of information flows is specified. The flows form an information space of the state government and administration bodies. The main features of the subset are the amount of information flows, the behavior of document quantity change in flows, the nature of the mutual influence of documents of various flows. The amount of information flows is specified according to the problem of control loops building. The behavior of document quantity change is limited by linear, exponential and logistic dependencies. Linear and nonlinear models of mutual influence of information flows are built. The models are based on the analogy of documents with the population, which is used in the modern scientific literature in the broad sense. Linear models are formed by a system of differential equations of the first order with constant coefficients. The total ordering of the solution is given, analytical results are obtained for some options. Nonlinear models are formed by the Lotka-Volterra equations for two information flows. The behavior of models near stationary points is specified with a restriction on the number of documents and without limitation.Information space, document flows, logistic model, Lotka-Volterra equations.
 2019_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 K. Vasilev, L. Korolev
 Estimation Of Varying Coordinates Of the Group Of Autonomous Vehicles The problem of integrating the estimation of own and mutual coordinates of different accuracy for an arbitrary number of independent devices considering impact of external indignations of different intensity is solved. The integration possibility of aircraft navigation parameters is considered in two ways. The first algorithm uses the vector linear Kalman filter to increase the accuracy of the dynamically changed coordinates of the group of unmanned aerial vehicles. The second method consists in dynamic estimating using the quasioptimum two-stage procedure that includes static assessment of coordinates and Kalman filtering. Expressions for detecting the covariation matrixes of integration errors are obtained by two methods. The efficiency of methods for estimating the navigation parameters of the group of unmanned aerial vehicles is compared under different initial conditions in a generic form and for the application case of the existing navigation systems. The results of comparative analysis of efficiency of two considered approaches are given.Estimation integration, vehicle coordinates, model of observations, stochastic equation of a state, Kalman filter, covariances of mistakes.
 2019_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 Mathematical Modeling Of Nonlinear Dynamics Of the Pipeline In the work, various nonlinear mathematical models are proposed that describe pipeline vibrations. Models are presented that take into account only the transverse deformation of the pipeline, and models that take into account the longitudinal and transverse deformations. All models are described by partial differential equations for unknown strain functions. The numerical-analytical solution is based on the Bubnov-Galerkin method. Based on model equations, a numerical experiment was conducted for various parameters of a mechanical system, which showed a small difference in dynamic characteristics for different models. A functional of the Lyapunov type was constructed for one of the models, on the basis of which the analytical conditions for the dynamic stability of the pipeline were obtained. Also, mathematical models of the dynamics of the pipeline are proposed taking into account the delay of power and (or) inertial characteristics.Pipeline, deformation, dynamics, stability, nonlinear model, partial differential equations, Lyapunov functional method.
 2019_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. Vasilev, P. Fediunin, M. Beliaev, A. Vasilev
 Simulation Of Spatial-Temporal Modeling Of Ground Target Moving Process One of the important tasks solved by the automated control system of aircraft during combat operations is to bring timely and reliable information about the ground target to the crews of attack aircraft systems. The delay of information in the communication channels leads to its aging, as a result, aviation management can be less effective. Considering the impact of delay has a comprehensive solution, which is implemented in practice by various methods and means. One of the known effective means are extrapolators. Authors consider a scientific-methodical approach allowing to research the extrapolators in the loop by mathematical modeling. The models developed in the framework of the proposed approach simulate the movement of a ground target on a real road with known geometric characteristics and road conditions. A distinctive feature of the models is that the results of processing and analysis of data obtained from geographic information systems are used in the process of their construction.Simulation modeling, message delay in the communication channel, maneuvering ground target, ground target motion model.
 2019_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 D. Zhukov,
 Analysis Of Classification Quality Criteria For Diagnostics Of Technical Object Operation When predicting the technical object health based on the known indicators of its previous operation, the problem of binary classification of the object state is solved. This problem may be solved using the machine learning methods, and due to imbalance of classes, the most reliable diagnostics quality measure is the F-measure. As a rule, the healthy-state data amount contained in the set of the use cases based on the results of object operation exceeds the unhealthy state data amount. Values of this measure are random variables as they are estimated using validation dataset formed in a random manner. The study showed that the distribution of this measure both for basic classifiers and for aggregated classifiers is close to standard one. A specific example demonstrates that the average value of F-measure in aggregation process exceeds the similar value obtained using the basic classifiers.Technical diagnostics, healthy state, performance indexes, machine learning, aggregated approach, classification quality criteria.
 2019_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A. Khusainov, A. Glushchenko, I. Salakhutdinov, M. Volkov
 Optimal Choice Of Recovery Technologies For Waste Lubricating Oils A technique for an optimal choice of technologies set for recovering the performance properties of waste lubricating oils based on dynamic programming has been described in the article. Each variant of technological operation has a different productivity and costs, also it is characterized by a specific sequence of quality indicator changes for the oil recovery. Authors make a choice of the sequence and content of technological operations which provide the given quality indicators for the recovery of oil performance properties with the lowest cost of labor input and implementation time. A composite indicator has been adopted as a target function which considers the productivity and cost for the oil recovery. The technological process is considered as a changing function of present value for the technological operation in case of its constant implementation time and function of time operation changing in case of its constant present value. According to dynamic programming methods, the use of the system of data on each technological operation stage allows obtaining the recurrent equations to determine the optimal technology with minimal present costs and time for the technological operations implementation. The solution of obtained equations results in the data array. The data analysis allows choosing the technological operations with optimal balance between its implementation time and present costs. The proposed optimization technique can be used in the development of the technological processes of any other type of production.Recovery technology, technological operation, optimization, dynamic programming method.
 2019_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A. Andreev, O. Peregudova
 Robust Motion Stabilization of a Mobile Robot with Omny-Wheels The modelling as well as the design and widespread use of wheeled mobile robots in the industrial and social spheres is one of the areas of rapid development of robotics. A sufficiently large class of such robots consists of wheeled robots with roller-bearing or omni-wheels. A distinctive feature of the design of such wheels consisting in the fact that the rollers are fixed to them according to a certain scheme allows the robot to move in any direction without a prior turn. This achieves high maneuverability compared to other wheeled carriages. The paper investigates the trajectory tracking control problem of a mobile robot with three omni-wheels and with an offset center of mass, i.e. when it is assumed that the center of mass of the robot does not coincide with the geometric center of the platform. Previously, such a problem was not considered. The paper substantiates the control structure that provides tracking of a given trajectory, including taking into account the delay and discreteness of the signal in the feedback. At the same time the control has the property of robustness which consists in the fact that its parameters do not depend directly on the mass-inertial parameters of the system and the tracked trajectory. The controller is constructed only by using the values of the system parameters bounds. The result has been achieved on the basis of the development of direct Lyapunov method in the study of the stability of non-autonomous systems obtained in the previous papers of the authors. The results of numerical modeling of the problem studied are presented.Wheeled mobile robot, robust control, stabilization, trajectory tracking, Lyapunov functional.
 2019_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 I. Davydov, D. Kozlov, S. Shakhtanov, M. Shibaeva
 Permutation Decoding in the System of Combinations Code Designs in the Evaluation of Biometric Data State-of-the-art telecommunication systems and means of data protection against natural and anthropogenic interference in the form of redundant codes are increasingly used in various applications related to the processing of biometric data. A large volume of publications in this subject area is devoted to codes with a low density of parity checks, polar codes, turbocodes with iterative data transformations that implement the algorithm of "belief propagation". These code constructions provide the required probabilistic characteristics but the procedure of decoding such codes takes long time intervals, which is unacceptable in terms of the duration of the cycle of biometric data management in systems critical to time delays. The paper proposes to use the principle of permutation decoding (PD), which is applied to systematic block codes. This method allows to fully use the corrective capabilities of redundant codes but in the classical interpretation requires cumbersome matrix calculations, which does not allow to use the positive properties of the method for error correction. The complexity of the computational process is excessively high. Therefore, to reduce the negative effect in the PD system, it is proposed to use the cognitive principle of data processing at the channel level, which significantly reduces the complexity of the decoder implementation and ensures the use of PD in the control systems of biometric data of subjects, for example, in the automation of transport security processes. Special attention is paid to the combination of codes in the format of cascade coding. For the first time, a description of such a scheme is given for polar codes and nonbinary Reed-Solomon (RS) codes.Soft symbol solution, permutation decoding, cognitive map decoder, concatenated code.
 2019_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Artificial intelligence.

 M. Samoilenko
 Matrix-Iterative Method of the Blurred Images Restoration A new method of the picture-original restoration from the blurred image is proposed. This method is based on the matrixiterative method developed by the author for solving the simultaneous linear algebraic equations. When implementing the image-restoration method, the author uses a prior information specified. It is assumed that the intensity of minimum background values of this image as well as the point spread function are known. The task of image restoration is resulted in the solution of an underdetermined system of linear algebraic equations. A pseudoinverse technique of its matrix is a known solution of the simultaneous linear algebraic equations. The well-known image restoration method based on this solution is also given. The author compares the image restoration by the use of this well-known method and a new matrix-iterative method based on computer simulating. It is shown that the matrixiterative method provides almost exact restoration under certain conditions. Such condition is a low occupation level of an image being filled up with objects if there is a high occupation level of an image being filled up with background values. The additive noise impact and an expected uncertainty were not considered.Simultaneous linear algebraic equations, matrix-iterative method, image restoration, point spread function, pseudoinverse technique.
 2019_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Artificial intelligence.

 V. Kozhevnikov
 The Method of Mathematical Modeling of Cognitive Digital Automata An approach to solving the problem of mathematical modeling of cognitive digital automata (CDA) is proposed. The task of formalizing the concept of the cognitive nature of the CDA mathematical model comes to the fore. The cognitiveness (cognition) of the mathematical model is determined by the possibility of learning and generating solutions that are not provided for in the learning process. A special feature of CDA is that the description of the neural network (NN) structure is used as a structural circuit of the automata, and the logical function "NOT-AND-OR" is used as the model of the neuron. In the case of the feedbacks formation from the output to the inputs of the neurons, the model of the neuron is a binary trigger with a logical function "NOT-AND-OR" at the input. As a tool for constructing a mathematical model of CDA, a mathematical apparatus of Petri nets (PNs) is proposed: marked graphs, inhibitory PNs and PNs with programmable logic. The mathematical model is builton the basis of the representation of the CDA in the form of the state equation of the PNs from the class of Murat equations (matrix equations) or a system of linear algebraic equations. The task of formalizing the concept of cognitiveness (cognition) is solved as a result of the logic synthesis (learning) of the initial structural circuit of CDA or the formation of the formula (network algorithm) of CDA. At the same time, the possibility of forming a formula (network algorithm) of CDA depends on the critical mass (quality) of training sets and training algorithms. Hence, the task of generating the minimum set of training sets for a given CDA function or experimentally determined function takes on particular importance. Forecasting or generation of solutions, in turn, is performed on the basis of the mathematical model of CDA obtained in the learning process.intellectual control system, cognitive digital automata, artificial intelligence, neural networks, machine learning, cognition, Petri nets, equation of states, mathematical modeling, synthesis, generation, analysis, logic.
 2019_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Artificial intelligence.

 I. Egorov, A. Moiseev,
 Models for Creating the Special-Purpose Mathematical Support of Computer-Aided Control Systems Authors provide reasons to a promising outlook for creating a technology for the development of special-purpose mathematical support of the computer-aided control system in order to improve the management based on process automation of content-related information processing and decision-making support. Different special-purpose software components as well as their development stages are analyzed. A block diagram of special-purpose mathematical support creating that includes production volume data at each stage and intensity of its growth and decrease. Linear differential equations build the mathematical models for creating the special-purpose mathematical support. Analytical decisions have been made, curves demonstrating the production volume change at all stages are provided. For mathematical modelling the processes of special-purpose mathematical support creating and decision-making support, authors use the Lotka-Volterra equations that demonstrate the creative behavior of designers’ work. The equations obtained are examined for stability. Authors detect approximate decisions. The models built are designed for optimal source distribution among development stages of all the special-purpose software types.Special-purpose mathematical support, design technology, mathematical modelling.
 2019_ 2

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.

 A. Smagin, I. Radionova, S. Karpaev
 Operating-resource Model of Technological Operations Distribution Based on the Implementation Means The article is devoted to the actual topic of designing route maps. At the heart of the route maps, the route for performing technological operations at the production site is laid. In the production process, production is often stopped due to imperfections in the route map, one of the reasons for which is the change of resources.In the article it is proposed to carry out the design of the technological route according to the proposed principles with the use of a two-pass two-component model as an increase in the productivity of the production process. The methodology is based on the principle of selecting the means for implementing technological operations on the basis of two interacting models, which make it possible to cover the process more fully from the point of view of resource provision and the performance of a technological operation using the example of chemical production.The proposed model allows the designer to choose the route of the technological process from the set of proposed options. An algorithm for designing and implementing a model in automated systems is presented.The offered algorithms allow to form design decisions, it gives the chance of their use for the subsequent processing and definition of efficiency.Formed by different criteria, technological routes provide many variants of the solutions obtained. The offered provides efficiency of improvement of quality of technological processes due to use of means of information support of maintenance of a set of operations close to an optimum choice of technical means of realization.Algorithm for designing design solutions, tool support, mathematical model, design methodology, operational- resource model, design of route maps of technological processes, technological processes, chemical production.
 2019_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 M. Samoilenko
 Reconstruction of the Point Spatial Coordinates in the Case of Normal Stereo Photography The article presents a solution for the problem of a point spatial coordinates reconstructing in a base coordinate system by its two stereo images. Author solves the problem for the case of identical cameras application which optical axes are mutually parallel and orthogonal to the stereoscopic basis. This taking photo is called in photogrammetry as a normal photographing. Author provides a computational simplicity of a point spatial position recovery algorithm. But in classical photogrammetry this computational simplicity is provided only under additional restrictions: cameras should locate at the same height, images should be horizontal and the base of stereoscopy - parallel to the horizontal axis of the base coordinate system. For another camera positions, it will be necessary to use additional spatial similarity transforms which complicate computations.Solution presented in the article differs from the photogrammetric method by its universality: neither additional conditionsare imposed to the positions of the cameras and images. And at the same time, it has computational simplicity comparable with the photogrammetric method of normal photography with additional restrictions. Methodologically, decision presented in the article is based completely on the application of vector-matrix approach from the problem formulation up to the final result. Structurally, it differs from the photogrammetric method by its symmetry with respect to of the cameras and images parameters: cameras are equivalent when determining a point spatial coordinates, while the photogrammetric solution is based on the coordinates on one image, the other one is used for the scaling factor determination.The universality of the presented solution and its computational simplicity are proved by the results of computer experiments.Stereo images, point spatial coordinates, central projecting, vector-matrix equation, photogrammetry, normal photographing.
 2019_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 D. Ganin
 Permutation Decoding in the System of Coherent Networks The principle of matching high-speed optical communication systems at the data link layer using permutation decoding of redundant codes is considered. The expediency of such an approach is proved when applying the cognitive data processing procedure. Author indicates the parameters of such systems. Considering the widespread use in data exchange systems and in automatic control systems, in computing systems and similar computing devices of non-binary noise-resistant Reed- Solomon (RS) codes, a subtle analysis of the complexity of decoding such codes using the permutation method is carried out. The estimation is made according to the number of code vectors of elementary arithmetic operations performed in the decoding procedure. Two approaches are compared: firstly, the classical principle of decoding RS codes, secondly, the permutation decoding method using a cognitive map. It is shown that the results obtained for rearrange decoding can be generalized for other code structures, including those implemented on the basis of binary codes. Various approaches to the formation of soft solutions for non-binary symbols of RS codes are presented and a likelihood ratio method is proposed which is based on comparing the obtained sequence of estimates of a non-binary code symbol with some predetermined reference set of estimates. The expediency of using the analyzed method in a number of important applied areas is proved.Coherent network, non-binary redundant code, cognitive map, fast matrix transformations.
 2019_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. Manzhosov, A. Samsonov
 The Functioning of the Lever Mechanism for Automated Capture of Solid The article is devoted to the problem of functioning of the lever mechanism in the automated capture of a solid body. In technological systems such mechanisms are used to lift and move solid cylindrical bodies. The task of the mechanism is an ability to hold a solid body due to friction forces in the capture zone. Friction forces in the contact zone of the driven link with the surface of the body exclude the possibility of breaking the connection between the solid and the driven link. The gripping force depends on the magnitude of the driving force and the parameters of the lever mechanism gripper. The model of the lever mechanism of capture is constructed. The ratio of the force at the leading link and the arising normal reaction in the contact zone of the driven link with the cylindrical surface is established. The influence of the mechanism parameters on the ratio of these forces is determined. The zones at which the force ratio reaches the lowest values are shown.Model of lever mechanism, automated capture, friction forces, angle of motion transmission.
 2019_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 I. Semushin, Y. Tsyganova
 Numerical Aspects of Far-end Crosstalk Cancellation in Vdsl Downstream A complexity analysis of computations involved in two precoding methods - Zero Forcing (ZF) vs. a Simplified Linear (SL) - in the context of a Very high-speed Digital Subscriber Line (VDSL) is presented in this paper. For the ZF-precoding technique, eight computing strategies have been compared, four of which entail the explicit calculation of inverse normalized channel matrices and other four do not. In addition to this analysis, SL-precoder complexity - based on the approximate matrix inversion-has been estimated. Both methods solve the problem of full or partial far-end crosstalk (FEXT) cancellation in VDSL downstream transmission. For this problem, the strategy avoiding the explicit matrix inversion was found to have the smallest number of multiplication/division operations. The analysis performed provides an opportunity for VDSL-designers to justifiably select a computationally attractive precoding strategy taking into account the necessity of adaptive power control for the input signals to the DSL-channel from the Central Station.Vdsl-системы, vdsl-systems, far-end channel crosstalk, downlink data transmission, zero-forcing precoding, simplified linear precoding.
 2018_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. Kovalnogov, R. Fedorov, L. Khakhaleva, A. Chukalin
 Mathematical Modeling and Numerical Analysis of Thermal Protection Effectiveness With Hemispherical Damping Cavities The gas turbine engine performance improvement is linked inextricably with the increase of the intensity of dynamic, aeromechanical and thermal processes, which, in turn, requires the development of systems and devices allowing to protect the most loaded equipment components. The most effective ways to protect surfaces from overheating are a convective cooling; the absorption and accumulation of heat by condensed substances; the cooling that operates on mass transfer principle; the radiation and electromagnetic cooling; heat-shielding coatings. One of the most effective ways to protect surfaces from overheating is a thermal protection in the form of film-like surface cooling based on the mass-transfer surface-cooling principle. This method is widely distributed and it proved to be effective. The paper considers the possibility of improving this method of cooling due to the impact on the boundary layer with hemispherical damping cavities behind the injection section of the cooler. A mathematical model is proposed, the numerical study of the thermal protection effectiveness by the use of hemispherical damping cavities is carried out. The possibility of a significant decrease of the turbulent heat exchange in the boundary layer and of the efficiency improvement of the thermal surface protection of ? by0.06 due to the use of hemispherical damping cavities has been established. The proposed method of thermal protection intensifying and numerical analysis of its efficiency will improve the gas turbine engines that are available for different applications of domestic industry for example in power generation sector, aircraft engineering as well as in shipbuilding.Hemispherical damping cavities, turbulent transport, mathematical modeling, boundary layer, thermal protection.
 2018_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A. Khusainov, A. Glushchenko, M. Volkov
 Developing the Model for Improving the Vehicles’ Operating Characteristics The process of developing the model to improve vehicles’ operating characteristics has been described in the article. The model development is based on the interrelation and reciprocal influence of the main elements of the vehicle. Since the internal combustion engine is the source of energy and the driving force, its characteristics has a direct influence on the operating properties of the vehicle. In its turn, they mainly depend on the nature of the working process course and engine parameters. Therefore, a change in the technical and operational characteristics of the engine will entail a change in the operating characteristics of the vehicle in which it has been installed. The information model of the engine parameters’ influence on operating characteristics of the vehicle allows us to find that, for certain operating time and fixed values of operating modes, an improvement of operating characteristics of the vehicle can be made by changing the technical and operational characteristics of the engine. At the same time, considering the operating model of the internal combustion engine in a form of a specific multidimensional and multilevel system, it was found that the working process in the engine and the design parameters of its mechanisms have the greatest influence on the change in engine parameters. The main work process takes place in the engine cylinder, so the parts of the cylinder-piston group will have the greatest influence on the change in the output parameters of the engine. The use of mathematical modeling in solving this problem allows us to develop a concept of improving the vehicle’s operating characteristics, to optimize the process of choosing the ways to modernize the engine and the vehicle.Vehicle’s operating characteristics, information model, multidimensional and multilevel system.
 2018_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 A. Ivanov, V. Baboshin
 Optimal Creation of Control Loops The creation process of control loops in a hierarchical automated control system is determined by a three-dimensional task of optimal distribution of control objects, monitoring software, and environment objects. Different variations of control loops are presented. An algorithm of random searching the optimal distribution of two-dimensional task with control objects and environment objects is described. The analytical approximation of algorithm is given. It was obtained by the orthogonal transformation and was implemented while planning the control objects usage with regard to changing their location in space. Based on the algorithm of the two-dimensional task distribution, the algorithm of random searching the optimal distribution of three-dimensional task for one of the variations when each loop was created by the specified elements that are not included in other loops was developed. Following the results of the undertaken analysis, it was found that task time at high dimensionality could not comply with the dynamic of situation changing. The way of applying the analytical dependence for task time reducing is shown as well as the corresponding algorithm is described. The findings of experimental studies carried out by the use of the developed software are given. The obtained results verify the theory.Control loop, distribution task, mathematical model, solution algorithm, analytical dependence.
 2018_ 4

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.

 A. Piftankin, A. Polovinkina, S. Tokmakov
 Mathematical Model and Algorithm for the Identification Task of Radio- Emitting Objects of Tactical Situation on Data From Ships of Task Force The article presents a mathematical model and algorithm for tasks of radio-emitting objects identification. The identification task partition into component parts is carried out. New approaches to the calculation of the radio-emitting object identification level from geometric and signal features will be found in the article. Authors propose a priority sequence of tasks to be solved based on practice of working with special information. A new mathematical model for constructing the identification evaluation function from signal features is developed. This model is not restricted to the assumption of thelinearity of this function. Algorithms for calculating the threshold values of object identification are presented. An algorithm for the radio object identification is developed under conditions of the computing experiment performed in the MATLAB environment. Following the results of the computing experiment, the algorithm has been defined more exactly, the positive outcomes of using the model have been provided.Passive radio aids, information identification, object identification level, machine learning method.
 2018_ 4

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling, Architecture of ship's system.

 A. Ivanov
 Distribution Laws of Stochastic Data Volumes on Hierarchical System Objects The article determines analytical dependences of information resource volumes on objects of the hierarchical control system from initial data volumes incoming to the system. The article considers the following variants such as control when initial data is executive orders from an object of high level; and situation data acquisition and analyzing when initial data comes from an object of low level. It is assumed output data volume at each level to be proportional to input data volume. The calculation procedures of distribution laws and numerical characteristics of stochastic data volumes of all objects at known distribution laws of initial data and random conversion ratio of input data into output data are specified. A simulation model of the hierarchical system is created which allows to obtain distribution functions and probability density of stochastic data volumes of all objects based on known numerical characteristics of the initial data. The simulation results are presented that demonstrate the principle possibility of obtaining distribution laws and their approximation by the normal law.Hierarchical systems, stochastic variables, distribution law, simulating modeling.
 2018_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling, Automated control systems.

 A. Kukin, A. Piftankin, A. Gutorov, A. Lushnikov
 The Model for Forming the Flight Profile of an Aircraft Using Dynamic Programming Tools The article deals with the process of forming the flight profile of an aircraft. Calculation and selection of the optimal flight profile of aircraft are some of the most common issues in the tasks related to the planning of aviation operations. The flight profile in the coordinates ‘range-altitude’ is a sequence of areas each of which corresponds to a specific program for changing altitude and speed. The construction of the flight trajectory of an aircraft is characterized by the work with a large number of nonlinearly varying dependent parameters and taking into account the restrictions imposed on flights: the permitted echelons of aviation flight altitudes, forbidden zones with unacceptable meteorological conditions, forbidden zones of action of enemy air defenses. These factors make it very difficult to model the specified process. The application of the mathematical apparatus of dynamic programming in solving this problem can allow the most efficient choice of flight modes of aircraft and optimize the process of forming the flight profile as a whole.Fighter aircrafts, flight profile, optimization algorithm, dynamic programming.
 2018_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling, Architecture of ship's system.

 O. Saverkin
 On the Efficiency of Trajectory Filtering in Fixed Coordinate System The article presents the analysis results of algorithms for estimating the motion parameters of the accompanying objects based on the application of the Kalman filter. It is shown that the application of some known algorithms is associated with the need to perform complex mathematical operations, and under certain conditions can lead to significant errors. It is established that the use of filtering in fixed coordinate system in the algorithm allows taking into account data on the direction and maneuvering of the object thereby increasing the accuracy and tracking stability. At the same time, simplicity of implementation is preserved when using the linear Kalman filter.Object tracking, trajectory parameters estimation, fixed coordinate system, kalman filter.
 2018_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling, Architecture of ship's system.

 I. Zhuikov, I. Nekhaev
 Application of Lp-structures When Constructing the Intelligent Test System Tasks of competence level are complex tasks for solving which is not enough only knowledge, so learning and testing systems should be able to simulate structures of gradually complicating tasks. In some cases, these structures can be modeled using mathematical lattices describing the structure of cases with additional attitude of complication. This article describes a model of the lattice of non-complication of cases for the subject domain. A method for specifying and constructing such lattice using finite LP-structures and applying operations of transitive closure on the lattice of clarification of case situations is proposed. In conclusion, the example of using this approach to construct intelligent test system of the ability to perform solve tasks of comparing numbers from the domain of arithmetic of natural numbers is considered. It is shown that this approach could be used for further analyzing the results of solutions and to construct a more pragmatic lattice of complication of cases and test tasks.Lp-структура, competency-based approach, intelligent test system, lattice of complication of cases, lp-structure.
 2018_ 3

Sections: Information systems

Subjects: Information systems, Mathematical modeling, Artificial intelligence.

 M. Samokhvalov
 Modeling the Brightness Dynamics of Thin-film Electroluminescent Capacitors The processes of excitation of luminescence of thin-film electroluminescent capacitors within the model of direct shock excitation of activator centers in the luminophore are analyzed. Mathematical modeling of the dynamics of the brightness of radiation sources is carried out on the basis of the solution of the nonlinear ordinary differential equation describing the kinetics of changes in the density of excited centers of luminescence in the phosphor film. A program for numerical solution of nonlinear equation of luminance dynamics by Runge-Kutt method using a computer is developed. It is shown that the duration of transient processes determined by the brightness waves reaches 8-10 periods of applied alternating voltage. In order to obtain high brightness levels of electroluminescent indicators, it is necessary to excite the indicator elements with suites of alternating voltage pulses, the duration of which must be at least the time of reaching the steady-state operation.Thin film electroluminescent capacitor, brightness, phosphor, electroluminescence, indicator.
 2018_ 3

Sections: Electrical engineering and electronics

Subjects: Electrical engineering and electronics, Mathematical modeling, Information systems.

 R. Brazhe, A. Savin
 Electric Characteristics of Sensing Elements of Resonance Nanosensors for Robotic Systems Based on Spiral Nanotubes Sensing devices of nanosensors for robotic and biorobotic systems based on separate spiral nanotubes draw an attention of researchers both as from the point of view of opportunities of their design with the use of the temporary nanotechnologies as from the point of view of their high sensitivity to external influences. Owing to deformation of nanocoil as a result of external influence, its impedance changes, and a shift of a resonant frequency appears. It is shown that the resonant frequency of such nanosolenoids can reach tens petahertz, and its shift can make the tenth shares of petahertz as a result of nanocoil’s length change for 1 percent.Spiral nanotubes, resonant nanosensors, impedance properties.
 2018_ 3

Sections: Electrical engineering and electronics

Subjects: Electrical engineering and electronics, Mathematical modeling.

 R. Brazhe
 Mechanical Characteristics of Electromechanical Resonators Based on Spiral Nanotubes In electromechanical resonators shaped as spiral nanotubes, two types of resonances such as an electrical resonance like in serial RLC circuit and the mechanical one like in a coil spring can exist. Both types of resonances can be used for designing the sensing devices of resonance nanosensors for robotic and biorobotic systems though their resonant frequencies strongly differ from each other. This paper deals with a comparison of electrical and mechanical characteristics of the electromechanical resonators based on coiled nanotubes. It is shown that the frequency of the displacement resonance in such mechanical oscillators can reach tens of gigahertz while the current resonance occurs at the frequencies reaching tens petahertz. The amplitude-frequency and phase-frequency characteristics of forced oscillations in the considered nanospirals are brought. It is shown that their mechanical figure of merit does not exceed several units and is comparable with the electrical one because of grate attenuation.Spiral nanotubes, electromechanical resonator, resonance characteristics.
 2018_ 3

Sections: Electrical engineering and electronics

Subjects: Electrical engineering and electronics, Mathematical modeling.

 I. Semushin
 Towards Robust Riccati Iterations for Lqg-optimal or Parameter-adaptive Estimation and Control Processes The paper aims at the development of robust and efficient computational algorithms for stochastic linear control based on scalarized square-root implementations. In the capacity of starting point, it uses the classical (formal) solution to the control problem known from the three-decker monography Stochastic models, estimation, and control, Academic Press, 1979-1982, by Peter S. Maybeck. The mutually time-inverse Riccati iterations being a core part of the solution, are interpreted in a uniform notation as the two-stage update processes. For them, a transition to the two kinds of scalarized algorithms - direct and inverse, is performed to introduce into consideration a scalarized filter and scalarized regulator and avail ourselves of the opportunity to go into the question of numerically stable square-root computation designs for Riccati iterations. The paper demonstrates one possible configuration in the form of the Potter-style algorithm. That establishes the new direction in constructing robust LQG-regulators for control as being based on many advances in robust filtering.Lqg-control, square-root algorithms, finite-horizon discrete-time control, scalarization.
 2018_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. Sergeev, S. Rezchikov
 The Optimization of Procedures for Measuring the Semiconducter Devices’ Paramters of Low-freqency Noise Influenced By White Noise The brief analysis of techniques for measuring the parameters of low-frequency (LF) noise with 1/f?-type spectrum has been proposed. The estimation of measurement error of power spectral density (PSD) and ?-rays spectrum index are given by taking into account the influence of white-noise level. Based on the results of noise spectral power density measurements implemented at three frequencies when series and parallel filtering, authors propose procedures of measuring the index of ?-rays spectrum that minimize a total inaccuracy of ? value determination. The essence of optimization in case of serial filtering reduces to the optimum distribution of preset overall measurement time between measurements at the first, second and additional frequencies in case of the given frequency ratio, and when parallel filtering, to the determination of the optimum frequency ratio of measuring the noise PSD in case of the preset overall measurement time. A systematic measurement error of ? value has been estimated while implementing of various measurement procedures depending on ? value. The estimations are presented in the article. It is shown that the optimization of measuring procedures allows to reduce an error of the ? value determination by 1.5 to 2 times.Low-frequency noise, power spectral density, index of spectrum form, measurement, error, optimum procedures.
 2018_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 I. Ukraintsev, V. Kalnikov
 An Alternate Bayesian Approach to the Detection of an Adaptive Decision Threshold Scheme for the Receiver At Decameter Radio Links The article deals with an approach to the determination of the decision threshold scheme of a receiving device in decameter radio link, which implements the alternative Bayesian method. In contrast to the classical approach when the decision threshold scheme is determined with the assumption that the probability density function (PDF) of the received signal is subject to the Gaussian low, an approach based on the current recovery of instantaneous values of the received signal envelope in each distribution path is proposed. The PDF recovery algorithm is based on the nonparametric Parzen-Rosenblatt density estimation method. The estimating is carried out during a specified communication session. In this case, the most probable values of the signal (mode) are determined if the noise interference is absent and present, the decision threshold scheme is established in accordance with the real situation on the communication line. Then, on the basis of the mode shift, a decision is made about the signal-error probability. On the basis of simulation modeling, the efficiency of the approach is shown when operating at decameter radio links working under nonparametric prior uncertainty relative to signals and interference.Signal depression, instantaneous values of the received signal envelope, parzen method of the probability density estimation, mode, decision threshold scheme of a receiving device, error probability.
 2018_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

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