ISSN 1991-2927

## Keyword: "mathematical model"

 D. Grigorev, T. Maslennikova, A. Piftankin, A. Polovinkina
 The Mathematical Model of Air Defense Control Process The article deals with problems on shipborne anti-aircraft defense (AAD) system control process. The development of a plan for distribution of shipborne air defense systems through enemy objects is a one of the main stages of this process. The distribution plan represents an assignment array, the element of which includes identifiers for the air object and AAD facilities and is assigned for that air object. The distribution plan is generated with ranking of air objects on a danger level, evaluating the capabilities or efficiency of the AAD facilities assignment to air objects, and generating the plan of AAD facilities distribution through air objects according to the given efficiency criterion. When solving this problem, it arises the necessity of considering not only the actual state of the system but the predicted one. Authors suggest a mathematical model that considers jointly planning processes (problem solving on the predicted state) and control processes (problem solving on the actual state) of AAD facilities. The model takes into account the using of multiplex means and their loading features as well as the dynamics of evolving events.Anti-aircraft defense (AAD), mathematical models, anti-aircraft weapon, distribution plan, assignment criterion.
 2019_ 2

Sections: Automated control systems

Subjects: Automated control systems.

 A. Ivanov
 Construction and Application of an Analytical Approximation of Three-dimensional Distribution The algorithm and software for solving a three-dimensional distribution problem in the forming of control loops are developed. Experimental research has been carried out. The dependence of the solution time on the dimension of problem determined by the number of control objects, observation means and environmental objects that form control loops has been obtained. A mathematical model of the control loop formation is constructed with the choice of optimal values of the adjustable parameters of control objects and observation means. A solution algorithm is described generally with the optimal distribution being performed at each step of searching the optimal values of adjustable parameters. A solution algorithm is proposed on the basis of an analytical approximation of the three-dimensional distribution, which ensures the practical implementation of high-dimensional problems with restrictions on time. An approximation equation for the three- dimensional distribution is obtained using an analytical approximation of the two-dimensional distribution. The equation was verified with experiments proved that it is possible to use it in high-dimensional problems. A mathematical formulation and an algorithm for solving the problem of control loop formation are given based on the mobility of control objects and observation means.Control loop, three-dimensional distribution, mathematical model, algorithm for solving, analytical dependence.
 2019_ 1

Sections: Automated control systems

Subjects: Automated control systems.

 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.

 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.

 D. Kharkin, I. Efimov
 The Mathematical Model and the Creation Method of the Illuminations Module of Liquid Crystal Panels on the Basis of Colored Leds The article considers construction of a module of illumination of liquid crystal panels on the basis of colored RGB LEDs. The algorithms of LED control for providing required illumination characteristics of liquid crystal modules are described. The algorithms’ adequacy was examined experimentally. The article also covers questions of influence of some characteristics of LEDs and constructive elements on illumination efficiency factor. The obtained mathematical models and algorithms allow to automate the development process of LED illuminations with forecasted characteristics. The ability to select elements with required constructive parameters for the specific LED illumination at the initial stage of development is appeared.Mathematical model, led illumination, disperser, control algorithm.
 2017_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling, Automated control systems.

 A. Ivanov
 Mathematical Models for Knowledge Management in Design Organizations The article considers problems of knowledge management in an organization involved in automated systems design. Knowledge is defined as information used in a productive process. The article shows that the key moment is availability of formalized models and unformalized methods for obtaining design solutions. The author gives examples of knowledge applied in organizations for designing automated management systems with the use of corresponding models. The mathematical models of sequential transformation of data into information, information into knowledge, knowledge into design solutions are developed as Lotka-Volterra linear differential equation systems. Situations of data occurrence from external and internal data sources, and deterioration of data, information and knowledge are considered. Analytical solutions for linear systems were obtained, researches of stability with the use of Lyapunov method were held, types of critical points were defined. The main trends of the knowledge management system were specified in order to gain competitive edge of the developing products.Design organization, automated systems, knowledge management, mathematical models.
 2017_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Automated control systems.

 S. Karpaev, S. Larin
 Building the Model for Balansing Industrial Forces of Multinomenclature Production The article offers a formalized model for constructing issue-related production plans (IRpp) on the basis of automated verification of process operations (pO). It reflects the mathematical algorithm for calculating the load distribution on working centers with reference to the specific equipment and performers as well as the search and finding algorithm for the interchangeable parts in designing pO of a business-process. The basic requirements for the implementation of the proposed model at the enterprise with multinomenclature production are described. The authors show the expediency of using this approach in integration of information flows of the system for automation of production technological preparation design and the system of operational and scheduling planning in design of production capacities load. As a result of the model implementation (on the basis of 1c: Enterprise 7.7) and carrying out a series of experiments, a reasonable conclusion about the effectiveness of the proposed scheme of developing IRpp for enterprises manufacturing multinomenclature products.Design of work centers load, mathematical model, planning system, issue-related production plan.
 2016_ 3

Sections: Computer-aided engineering

Subjects: Computer-aided engineering, Information systems.

 G. Antsev, A. Krasnikov, E. Novikov
 Methodological Aspects of Designing Naval Integrated Management Systems The paper is devoted to methodological aspects of the creation of a special software for integrated management systems (IMS) of the Russian Naval ships [1-3]. In the context of system analysis, the problem of developing control solutions for semistructured problems in complex tactical situations is considered [4-7]. The authors substantiate the value of special mathematical models development for the problem situations analysis. The ability to formulate the problem of optimal (efficient) control solutions generation more clearly is occurred on the basis of such analysis. The examples of using the analytical models of combat confrontation predictive modeling in information control system quality assessment are given. The basic principles and steps of the methodology for constructing mathematical models of semistructured problems of practical interest and the approaches to the choice of criteria and indicators of information control system quality assessment are proposed. The authors use the methods of system analysis, operations research, decision-making, queue systems, computer mathematics modern systems.Methodology, integrated management system, mathematical model, queue system, system analysis.
 2016_ 2

Sections: Automated control systems

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

 V. Moiseev, M. Sorokin, I. Efimov, T. Davydova
 The Mathematical Model of the Static Pressure Flowing Reciever The article considers the matters of constructing mathematical models of the static pressure following receivers (SPFRS) designated for sensing static pressure on helicopters in a range of airspeeds to 250…350 km/h. SPFRS consist of contracting and diffusing parts. The mathematical model of SPFRS was developed in accordance with results of experimental researches for defining static pressure, dynamic pressure, speed, speed inaccuracy, altitude inaccuracy. The adequacy of the obtained mathematical models is checked through the comparison with the results of experimental researches. The models allow getting reliable data at the contractor convergence angle in 30-70 degree, the diffuser aperture angle in 8-14 degree, the diaphragm coefficient in 0.15-0.45, windblast speed in 20-250 km/h. The influence of separate components (a contractor and a diffuser) on SPFRS pressure coefficient and correlation between experimental data and the results obtained with the mathematical model are considered. With the use of the obtained mathematical models, the process of developing receivers with predicted metrological characteristics can be automated. The ability to take up receivers with required form factors for the specific control object on the original development cycle promptly has been appeared.Mathematical model, static pressure following receiver, contractor, diffuser.
 2016_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling, Automated control systems.

 S. Ageev
 Data Mining Methods for Information Security Risks Management of the Special Purpose Protected Multiservice Networks The data mining methods using for information threat risks management of the special-purpose protected multiservice networks (SPMN) elements are proposed. The fact that the process speed in SPMN, its variety, inaccuracy, and imperfection as well as a high aprior network element data dimension necessitates the application of intelligent techniques for data processing and management is explained. The factors effected on the SPMN information security management cycle time are analyzed, a unified metric for the threat assessment of SPMN elements information security is proposed. A unified mathematical model for the procedure of information security threat clustering, ranking, and classification is developed, its performance criteria are evaluated. The research results of this mathematical model are presented. Threat estimation rules for the special-purpose protected multiservice networks are formulated. The achieved results of mathematical modeling are analyzed, the recommendations of practical application are provided. The similar methods and algorithms application in combination with intelligent agent technology allow to increase the efficiency of SPMN information security management. Directions for future research in this subject domain are defined.Protected multiservice network, efficiency of the management, tmn-model, mathematical model, intelligent control, fuzzy inference, knowledge base, membership function, fuzzy data, linguistic variable.
 2015_ 2

Sections: Information systems

Subjects: Information systems, Mathematical modeling, Artificial intelligence.

 D. Parafeynik, D. Sushchenkov
 Application of Mathematical Tools of Semi-markovian Process and Jackson’s Network Approach in the Simulation of Air Defence-missile Defence (ad-md) of All-arms Forces The usage of up-to-date integratabilities of control, communications, intelligence, and attack weapon systems, and of the enhancement of their interaction level by means of the implementation of principles of the new “network-centric” concepts specifies the necessity to conduct thorough investigations, including ones in the field of mathematical modeling. The article presents an issue regarding a timely character of over-the-horizon acquisition of air targets and transmission of target designation from external systems to networks of space-distributed all-arms forces and means. This article provides a mathematical model that represents the mode of control of Fleet all-arms forces, integrated in the unified system by means of the complex control systems network architecture and controlled forces, when a group of ships executes an AD-MD mission using space-based reconnaissance systems, satellite communications and shore-based intelligence information centers. The index system that enables to estimate the effectiveness of all-arms forces operations with regard to the evaluation of timing data of random processes execution in the control network is elaborated. The mathematical simulation is executed to the benefit of development of military-oriented computer-aided control systems.Mathematical model, anti-ship missile, antiair warfare, anti-aircraft missile, space reconnaissance assets, measures of effectiveness, jackson’s network approach, theory of queues, kill probability, time distribution function.
 2014_ 4

Sections: Automated control systems

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

 V. Belov, A. Butkina, A. Shamaev
 Mathematical Simulation of Power Conversation Systems for Micro Grid Mathematical model of AC/DC/AC converter with energy storage device is developed on the base of the bridge element concept. This model is intended for the analysis of conducted interference at the designing stage of micro Smart Grid, which contain AC/DC/AC converters, as well as for the emulation of the control object at the software development stage of microcontrollers.Bridge element (B-element) is a generalized model of the m-phase bridge converter of electric power, in which transistors are modeled by ideal switches. Rules to represent a graph of the equivalent circuit of AC/DC/AC converter with energy storage as a set of subgraphs corresponding standardized bridge elements are developed. Application of these rules provides correctness of algorithm functioning of forming and solution of differential equations of the equivalent circuit at any state of the switches automatically.Computational aspects of the algorithm have been investigated on the example of mathematical simulation of AC/DC/AC converter with MPI distributed computing technology. Preliminary results showed that increasing of the simulation speed may be achieved by application of parallel computing technology for solution of the complete differential equations system formed on the B-element base. Element-wise forming and solution of differential equations systems does not increase the computational efficiency. Additional studies are required for final confirmation of these results.Smart grid, smart grid, power converter, mathematical model, power quality, parallel computation.
 2014_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 V. Moiseev, M. Sorokin, I. Efimov, N. Makarov
 Mathematical Model for Pitot-static Probe The article deals with mathematical modeling problems of the air pressure probes composed of the front cylindrical receiving tube having inside conical flow stagnation chamber and static pressure holes. Basic mathematical models for the air pressure probes were derived from the mathematical modeling intended for determination of static pressure, dynamic pressure, velocity, velocity and altitude errors. The adequacy of the received mathematical models is checked by comparison against the experimental research findings. Experimental studies were carried out in the T-129 wind tunnel of TsAGI with nozzle-jet simulator. These models allow to get true data at such parameters as the cylindrical tube radius over the range 6.5 to 8.5 mm, start tube distance to the static pressure holes of 45 to 70 mm, downwash angle of 0 to 90 degrees, incident airflow velocity at 50 to 250 kmh. The received mathematical models enable to automate the engineering process of Pitot-static probe with metrological performance predictions. This gives the ability to make a quick selection of probes with design parameters required for a specific control object at the initial development stage.Mathematical modeling, pitot-static probe, mathematical model.
 2014_ 1

Sections: Mathematical modeling

Subjects: Mathematical modeling.

 S. Ageev, I. Saenko, Y. Egorov, A. Gladkikh
 About Development of Mathematical-model System for Control of Protected Multi-service Network The article deals with basic approaches to development of mathematical-model system for control of protected multi-service networks. It grounds why intellectual methods for control of protected multi-service systems are required, and presents basic principles of level-sensitive mathematical modeling of operational tasks of control of protected multi-service network. The authors have suggested solutions for interaction of level models as well as coordination of efficiency factors for differentlevel models.Protected multi-service network, telematic network services, automation of control, tmn model, mathematical model, coordination of control.
 2012_ 3

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Mathematical modeling, Automated control systems.

 A. Ivanov
 Optimal Allocation of Resources in a Hierarchical Control System The article gives a sequence to build a mathematical model for optimal allocation of resources in hierarchical control systems on basis of an experimental deduction of dependencies between efficiency of control agencies and objects and allocated resources. It also cites flowcharts of a program for the calculation of the dependencies, and examples of the solutions.Planning, hierarchical systems, mathematical models, efficiency.
 2011_ 3

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Mathematical modeling, Automated control systems.

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