APPROXIMATION OF EVOLUTIONARY DIFFERENTIAL SYSTEMS WITH DISTRIBUTED PARAMETERS ON THE NETWORK AND MOMENT METHODS
The paper considers evolutionary problems underlying the mathematical description of oscillatory and hydrodynamic processes in network-like objects (waveguides, hydraulic networks, etc.). The main attention is paid to the analysis of the properties of the elliptic operator (the one-dimensional Laplace operator) with distributed parameters on the network, establishing the spectral completeness of the system of eigenfunctions in the class of square-integrable functions. Conditions are obtained that guarantee Neumann stability (spectral stability) of difference schemes for evolutionary problems; a solution to the moment method control problem is presented. The methods for studying evolutionary problems are based on the properties of a positive definite elliptic operator: a system of eigenfunctions forms a basis in the space of functions summable with a square; series in the system of eigenfunctions admit a priori estimates of the solutions of the evolutionary problem; approximation of an elliptic operator reduces it to a finite-dimensional operator in a finite-dimensional space of grid functions with a natural Euclidean norm, which (a finite-dimensional operator) approximates the original with any predetermined accuracy in the sense of the norm of the space of functions summable squared. For evolutionary problems, an explicit first-order approximation scheme on the graph grid (parabolic system) and an explicit second-order approximation scheme (hyperbolic system) are used. The oscillatory properties of the obtained operators are established, similar to the classical oscillatory properties. For difference schemes of parabolic and hyperbolic systems of equations, conditions are obtained that guarantee countable spectral stability (stability in the sense of Neumann) and, therefore, the possibility of obtaining analogues of A.F. Filippova on the convergence of difference schemes in terms of approximation steps of a graph grid. To illustrate the applicability of the approach used, the control problem is considered – the translation of evolutionary systems of parabolic and hyperbolic types from given initial to given final states; conditions are obtained that guarantee the controllability of the systems under study.
Keywords: laplace operator on a graph, evolution problems, approximation, difference schemes, stability, convergence, method of moments.
OPTIMIZATION OF “LAST MILES” TO REMOTE ACCESS NODES BY APPLICATION OF LCAS TECHNOLOGY
E.S. Maklakov, A.A. Gulamov
The article deals with the problem of construction and further operation of the last miles of departmental communication networks to the point of presence of Telecom operators, as well as the option of optimization of optical departmental networks to remote access nodes at the point of presence of Telecom operators. The structural location of network elements is described. Outlines the key used topology access networks. The topology of the “ring”is described. The application of LCAS technology to increase the bandwidth of individual communication channels formed in the SDH network is considered. The analysis of efficiency of departmental communication networks with the use of LCAS technology and without it is carried out. The requirements for the organization of communication channels of domestic networks in the electric power industry by types of channels and transmission rates are indicated. The technology of organization of SDH network structure of frames and types of containers used for traffic transport in optical networks is described. The principle of operation of LCAS technology in optical networks is described in detail on the example of organization of cross-connections of VC SDH containers. A number of advantages of using this method of optimizing the last miles of departmental networks to the point of presence of Telecom operators, which in turn are confirmed by the experimental method, are determined.
Keywords: access node, last miles, transport network, synchronous digital hierarchy, data transfer.
ANALYSIS OF METHODS OF MODELING TECHNICAL SYSTEMS IN MATLAB
UDC 519.6, 621.3
Y.V. Bebikhov, A.S. Semenov, M.N. Semenova, I.A. Yakushev
The MatLab software package is considered from the point of view of a universal modeling environment for technical systems. The analysis of methods of mathematical, structural and physical modeling in MatLab using the library of blocks Simulink and application SimPowerSystems. For the study, an electromechanical system was chosen – a DC motor with independent excitation, as one of the most common for driving technological installations of cyclic action. With the help of a laboratory setup, a simulation model has been developed that allows you to evaluate, analyze and compare the results obtained during modeling with real data. To carry out the simulation, additional parameters of the DC motor were calculated, which include the active resistances and inductances of the armature windings and excitations, mutual induction, moment of inertia, design and time constants of the motor. Physical, structural and mathematical models are developed. The simulation results are obtained in the form of graphs of time dependences of the main engine parameters. A detailed analysis of the angular speed of rotation of the DC motor was made, since it is the main coordinate for regulation. Qualitative and quantitative characteristics of the transition process, such as control time, magnitude of overshoot, and the number of oscillations, were subject to assessment. During the evaluation and analysis of simulation results, the advantages and disadvantages of various methods of modeling technical systems in the MatLab software package were established. Conclusions are made about the universality of the MatLab environment for the possibilities of a detailed and accurate assessment of complex technical systems.
Keywords: modeling of technical systems, MatLab, Simulink, DC motor, angular rotation speed, transient, error.
BUILDING AND MANAGING INDEX OF DISTRIBUTED SEARCH ENGINE BASED ON *BFT CONSENSUS ALGORITHM
In this article, we consider an algorithm for building a search index of a distributed search engine that uses the consensus algorithm of the *BFT (Byzantine Fault Tolerance) family, as well as its reorganization caused by the addition or removal of nodes from the search cluster. The article describes the structure of the cluster, addition of data to the index, cluster reorganization algorithm, and also discusses possible related problems and their solutions. At the same time, the limitations imposed by the very nature of distributed computing and the need to comply with BFT requirements are considered. The value of the task is due to the increasing need to use distributed systems to solve different practical tasks, including the organization of search, as well as the need to adapt existing solutions to the conditions of distributed systems and to take into account the limitations imposed by them, as evidenced by the existence of active research in this area and the current in the market situation. The methods and approaches used in this work, with some modifications, can be transferred to similar tasks arising in distributed systems of other types. The results and materials of the article can be used to solve applied problems in the implementation of distributed computing systems, distributed search systems, distributed data storage systems.
Keywords: search, distributed systems, BFT consensus algorithm, load balancing.
SPATIAL DECOMPOSITION METHOD OF INTEGRATION AND COMMUNICATION SPACE TO BUILD NETWORK STREAMS
A.N. Baichorova, L.M. Elkanova
Development of scientific and technological progress leads to a rapid increase in dimensionality various networks, info telecommunication, electrical networks, routes, etc., which leads to the accumulation of a very large amount of both structured and unstructured data (Big) that require analysis and processing. The paper considers the method of modeling the optimal installation and breakdown of switching space tools predfraktalnyh theory graphs. Unlike all known methods of this joint approach in solving the tasks of posting and trace Highway (channel) is a part of the plane (plates). A method of recursive Division switching space mounting-with the creation of active-passive graph model. An important role in assembling and switching play breakdown “wall” between the spatial slices, as well as location on the walls of the transit points for authorizing the holding through them links (conductors). There is a possibility of a more flexible resource allocation “walls”, identifies linkages through Streams crossing ability “walls” and “are not conductors walls”, but use the notion of “beams”, “ligaments”, “streams” of links and the mathematical apparatus of flows in networks, graph or prefractal graph. The resulting dual graph of such a decomposition is called “envelope-Earl” has a lot of interesting analytic properties. To solve the problem of synthesis of this graph (network), in which the thread exists and satisfies all the input from the outside restrictions, the algorithm “vertushechnogo” Division INC on estimating the time zone for which the solution varies from O(Q2.33) to O(Q3).
Keywords: decomposition of switching, installation space, flows in networks, prefractal graphs, streaming algorithms
PARTICLE SWARM OPTIMIZATION WITH ADAPTIVE SOCIAL AND COGNITIVE COMPONENTS
Efficiency of solution finding by particle swarm optimization depends significantly on specific values of social and cognitive components used by a researcher. There is no known way currently to determine whether specific values of the components would provide maximal search efficiency in a particular case, or not. In order to eliminate this flaw, this article provides a modification of particle swarm optimization with adaptive social and cognitive components, which allows to fit particles movement to a particular problem during optimization process, thus removing the need of adjusting components manually. This adaption is based on genetic algorithms principles: it starts with a selection of the best performing particles, then crossover of their social and cognitive components with other particles, then mutation to provide some fluctuations of components. To evaluate algorithm’s performance a series of experiments on minimizing few test functions has been made. Minimums found by adaptive and canonical algorithms were averaged out and compared. Based on results, a statistical hypothesis that adaptive algorithm has better performance than canonical algorithm was confirmed. Provided research proves efficiency of adaptive particle swarm.
Keywords: mathematical optimization, particle swarm optimization, adaptation, genetic algorithms.
3D FACIAL SCAN REGISTRATION WITH FACIAL EDGES DETECTION
The relevance of this work is caused by need of high-fidelity non-rigid registration algorithm for facial scans. Despite the fact that over the past decade, a large number of various algorithms for 3d model registration were proposed, including models of a human face, the vast majority of them are unable to provide accurate face registration for lips and eyes. This work is intended to improve this situation by using a detector of facial boundaries based on deep learning, namely using convolutional neural networks. Usage of facial landmarks detectors (deep learning based or other algorithms) is not novel in the field of non-rigid registration. However such approach is not good enough for precise registration. Facial landmark annotation is ill posed problem in general case, due to ambiguity of landmarks position. For example, it is very difficult to put landmarks in the middle of the eye so that they are anatomically in the same place in different frames. In this work we propose an alternative method – facial edges detection for registration. Obtained results show the advantage of the proposed approach.
Keywords: non-rigid registration, 3d scanning, iterative closest point, facial edges detection, deep learning, convolutional neural networks.
MATHEMATICAL MODEL OF OPTIMIZATION OF THE NETWORK INFRASTRUCTURE OF A DISTRIBUTED ENTERPRISE SYSTEM ON A CLOUD, MISTY AND EDGE TECHNOLOGIES
This article describes the formulation of a mathematical model to optimize the structure of the computer network of a distributed corporate information system based on a multi-level topology. Multi-level topological structure allows you to present the network structure, which includes a detailed description of the relationships between such network objects as active equipment, workstations and servers at different levels of the model, to show as a whole a variety of aspects of data transfer management with support for QoS protocols, technical and software implementation, information space and management. As a result, the design of the computing network of the corporate system can be performed as the development of a single network infrastructure of distributed software and hardware, which includes interconnected and interacting subsystems that solve functional tasks for the management and planning of the enterprise activities within a single approach to achieve the goal of obtaining an optimal architecture and meet the complex system and functional requirements for performance, bandwidth, reliability, etc. The paradigm of cloud, foggy and boundary calculations is used, which allows to build a modern network infrastructure within the framework of the industrial IoT concept. The most typical example of the use of this paradigm can be intelligent power supply networks, distributed monitoring systems for the transportation of gas or oil products, distributed systems of an industrial enterprise. To solve the problem, it is proposed to use an approach based on a modified genetic algorithm. The results of the experiments are presented.
Keywords: multi-level topological structure of distributed corporate system, computer network, cloud computing, fuzzy computing, edge computing, genetic algorithm.
DEVELOPMENT OF SOFTWARE FOR MODELING A NETWORK WITH INHOMOGENEOUS LOAD
S.A. Laptik, F.N. Abu-Abed
This paper devoted to the development of software designed to simulate networks with heterogeneous load, with further determination of the characteristics of network traffic. Traffic pulsations, inhomogeneities of application flow form an uneven load in computer networks. The process of modeling networks before their direct design is of paramount importance, respectively, the development of software (tool) for modeling networks is an important task. The development of algorithmic and software tools for modeling network traffic greatly simplifies the process of researching computer networks and contributes to the development of recommendations for further redistribution of load between network nodes. Each model under development has its own limitations and the reliability of probabilistic simulation results, which depend on the chosen mathematical apparatus, depends on them. The apparatus of queuing theory allows analyzing the results obtained at the level of their average values, and simulation modeling allows monitoring changes in network traffic over the entire simulation period for a set model time. The developed software is based on the modification of the already existing classical algorithm for calculating the performance of computer networks with heterogeneous traffic. The algorithm allows to optimize the values of parameters aimed at improving the performance indicators of networks with heterogeneous load.
Keywords: modeling, computer networks, network traffic, networks with non-uniform load, performance.