Mathematical Machines and Systems. 2021 #3

ABSTRACTS


COMPUTER SYSTEMS

UDC 623.764

Sapaty P.S. Spatial grasp model for dynamic distributed systems. Mathematical machines and systems. 2021. N 3. P. 3–21.

More complex distributed and intelligent systems which relate to economy, ecology, communications, security and defense, and cover both terrestrial and celestial environments are being developed. Their efficient management, especially in dynamic and unpredictable situations, needs serious investigations and development in scientific and technological areas. Their traditional representations as parts operating by certain algorithms and exchanging messages are becoming inadequate as such systems need much stronger integration to operate as holistic organisms pursuing global and often varying goals. This paper is focused on a completely different paradigm for organization and management of large dynamic and distributed systems. This paradigm extends and transforms the notion of an algorithm for the description of knowledge processing logic. Moreover, it allows it to exist, propagate and operate as an integral whole in any distributed spaces which may constantly change their volumes and structures. Taking into consideration some organizational features related to dangerous viruses, as well as recent pandemics, this ubiquitous Spatial Grasp (SG) model is presented in the paper at philosophical and implementation levels, together with the introduction of special spatial charts for its exhibition and studies, which extend traditional algorithmic flowcharts towards working directly in distributed spaces. Utilization of this model for the creation of resultant Spatial Grasp Technology and its basic Spatial Grasp Language, already described in details in numerous publications, is briefed as well. Elementary examples of dealing with distributed networks, collective human-robotic behavior, removal of space debris by a constellation of cleaning satellites and simulating the spread of virus and vaccination against it explain SG advantages over traditional system organizations. Figs.: 22. Refs.: 23 titles.


  
      INFORMATION AND TELECOMMUNICATION TECHNOLOGY

  

UDC 621.537

Voloboev V.P., Klymenko V.P. On the issue of navigation of an aircraft on the radar field. Mathematical machines and systems. 2021. N 3. P. 22–33.

The paper considers a new approach to the search for information parameters of the radar field, the source of which is a radar with a real antenna aperture. Such aperture is necessary for the construction of a digital radar map of the terrain, applicable for the navigation of an aircraft along a trajectory that is close to being vertical to the Earth's surface. The article reveals the essence of the approach. Because of the development of analog-to-digital conversion of the gigahertz frequency range, it became possible to analyze the radar signal reflected from the underlying surface of the Earth and located on it objects in details. It has opened up new opportunities in the search for information parameters of the reflected signal (a video pulse). There have been obtained some new information parameters, such as intensity of the reflected signal from the object, duration of the leading and trailing edges of the video pulse reflected from the underlying surface of the Earth and located on it objects, distance from the aircraft to the underlying surface of the Earth. It is proposed to construct a relief map of a section of the underlying surface of the Earth and located on it objects in terms of a horizontal trajectory or a trajectory close to it. The paper analyzes a method for constructing a radar contrast map based on the intensity of the signals reflected from the underlying surface of the Earth and located on it objects. There have been proposed such information parameters as the height of an object and an estimate of the height of the slope of the underlying surface of the Earth which are independent of external conditions and which can be considered as the main elements for building a digital three-dimensional map of the area. The obtained results can be considered as a source material for theoretical and practical research in the sphere of development of an all-weather high-precision navigation radar system. Figs.: 4. Refs.: 22 titles.


UDC 004.89

The paper deals with the main issues of creating situational centers. Making decisions in complex systems is a very complex problem that can be solved using decision support systems. Solving management tasks at the state level, forecasting, analyzing in conditions of hostilities and a state of emergency, overcoming the consequences of emergency situations are intersectoral. These tasks are solved through the work of experts and analysts on the technological basis of decision support systems functioning as the part of situational management systems in the form of situational centers. Situational centers of the security and defense sector are designed to make management decisions on a complex, multifunctional governance structure, elements of which are often poorly structured and insufficiently formalized. Input information is incomplete, ambiguous, sometimes contradictory. Thus, the determination of the functional and organizational principles for the creation and development of situational management systems, based on these principles, is an urgent task. Today, the most important task for government agencies is to improve the efficiency of management activities based on comprehensive monitoring of the current situation and prompt response to its changes. The complexity and unusualness of the tasks facing management structures determine the need for proper scientific, intellectual, information and analytical support for their solution. Therefore, summarizing the international experience of creating and using situational centers in management structures, the article proposes a substantiation of the organizational and functional structure and gives recommendations for improving the decision support technology, as well as directions and prerequisites for creating situational centers for public authorities in the security and defense sector. Approaches to achieving compatibility of their work in a single network are proposed, if necessary, and the modes of their functioning are identified. Figs.: 5. Refs.: 10 titles.


UDC 004.02:004.5:004.6 351.863.1

In conditions of constant displays of aggression in various fields of activity, which is one of the most acute problems of our time, corresponding preventive measures are becoming increasingly important. In its turn, it requires the improvement of the methodological support for decision-making to ensure security and counter various kinds of attacks. At the present stage, the remaining slowness of identification of incidents and determining the scale of their development is a characteristic feature of security management. Methodological complexity of the procedures for assessing security risks and corresponding calculations is stipulated by the lack of appropriate methods, software and technologies on the market, which complicates the development of automated decision support tools. This paper offers a universal method based on a formalized model of the relationship between objects (resources), aimed at them threats and expected risks. This model is based on the «threat – object» binary scheme expressed in a bipartite graph and provides for the division of the graph into subgraphs. There is built another (third) set that corresponds to the safety model with full overlap and protection mechanisms as well. Simultaneous utilization of the elements of ontological descriptions increases the level of the method concreteness and a clearer understanding of the environment state. A matrix approach, which is closely related to graph models, is proposed for computations. The article provides some schemes of technological implementation of the obtained solutions based on office applications and designing a corresponding information and analytical system. The proposed method can be applied in automated systems in many fields of activity. Figs.: 7. Refs.: 17 titles.


UDC 519.21

The paper is focused on an information and telecommunication robot (ITR) that is a cluster of precision mobile mechanical objects (sensors or multisensors) that perform a common mission concerning either monitoring or protection of the territory or the coordinates of the search objects location.ITRs are equipped with wireless telecommunication systems and high-performance small-sized on-board computers that allow the use of cloud technologies and fog computing. A group of unmanned aerial vehicles (UAVs) that perform a common mission (such as searching for victims of natural disasters) and are equipped with interoperable wireless telecommunications systems can be considered as a flying ITR. Mobile sensor networks (robotic sensor networks and systems) are also considered as a possible technical implementation of ITR. From a theoretical point of view, these control objects can be classified as composite dynamic systems (CDS). The article also analyzes the notion of trajectories of composite dynamical systems that are called branched trajectories in the scientific literature. These trajectories consist of several sections of joint movement of CDS subsystems and some sections of their individual movement to the targets along separate branches of the trajectory. Analysis of the physical content of the phenomena that accompany the process of ITR (and especially of mobile ITR) functioning has shown that such clusters are under accidental influence. Therefore, stochastic CDS should be considered as a model of ITR functioning. To solve the problem of optimizing the process of stochastic CDS control, there arises a task of developing a method of stochastic dynamic programming with complete information about the vector of the ITR state. The article describes a solution to the problem of stochastic composite dynamic system control optimization, with an arbitrary branching scheme provided that complete information about the state vector is available. Refs.: 24 titles.


UDC 519.21

The paper describes sufficient conditions for determining the distribution of functionals of an n-dimensional Brownian sheet (Chentsov field) on a set with the dimension lower than the dimension of the field. The results have been obtained through the generalization of the well-known Doob's Theorem on the identity of the transformation of some Gaussian and Wiener processes in the case of random fields. It is known that the distribution of functionals of a Brownian sheet on the sets with the dimension lower than the dimension of the field and a set of suprema of a piecewise linear curve in particular requires dealing with rather cumbersome integrals that might be hard to estimate. The paper suggests an alternative approach to the problem and considers the probability of suprema of a Brownian sheet being less than a certain drift. The obtained results can significantly simplify the task of determining the distribution of functionals of a Brownian sheet by reducing it to the problem of finding distribution on parallelepipeds with the dimension lower than the dimension of the field. There is also illustrated the validity of the obtained theorem through modeling some Brownian sheets and comparing empirical probabilities with theoretical ones. For the simulations, there have been used the R statistical software. In order to model a Brownian sheet, there has been utilized a special algorithm allowing to model random fields with covariance function of a special form as well as their restrictions on sets of lower dimension (curves, piecewise linear curves). The corresponding R code is provided as well. Refs.: 15 titles.


UDC 004.93’1

An alternative approach to the processing of elements of linear discriminant functions for the classification of objects is proposed in the paper. This approach is based on the method of processing a vector array of data by differential slices which is distributed in the column of matrix representation of elements of discriminant functions. In its turn, it indicates the spatially distributed nature of the processing of matrix elements with dimension m × n, where m is the number of classes, n is the dimension of the input data vector. The linearity of the representation of each discriminant function in a set of discriminant functions allows not only to represent their terms in the form of matrix elements, but also apply to their processing some rules concerning such properties as associativity and commutativity of components (terms) of the sum. As a result, such complex procedures as multi-operand summation in the formation of each discriminant function are replaced. Moreover, it is followed by their comparison with each other with the aim of identifying the one with the maximum value. In each processing cycle of the proposed method, the basic operation is a simultaneous reduction in the magnitude of the elements similarity of the same name in the columns of the matrix, which allows determining the maximum value of the discriminant function. The operation of transposition (advancement) to the edge of all current zero elements in each row of the matrix is also involved. This approach is applied to linear discriminant functions as an apparatus of the statistical method of object classification. Consequently, according to the known decision rule, the maximum discriminant function determines the corresponding class to which the input object, represented as an n-dimensional feature vector, belongs. One of the options for the hardware application of such classifier is the decision support subsystem for medical diagnosis. Refs.: 15 titles.


                                   SIMULATION AND MANAGEMENT

UDC 004.5

Conducting intelligence activities is one of the main directions of ensuring national security of any state. This paper is devoted to some aspects of automation of normative and legal support of intelligence activity. The article considers some issues of ensuring the national security of Ukraine, the role and place of intelligence agencies in its provision; it analyzes recent research and publications on the issues related to the growing importance of intelligence in the modern world. The given paper substantiates the necessity of development of the automated system of normative and legal support of intelligence activity and formation in the structure of Ukrainian intelligence bodies a division of the intelligence activity automated normative and legal support which would be responsible for the centralized conducting of normative and legal information on the basis of uniform classification and coding standards. Intelligence support, as well as the processes of collection, accumulation, processing, storage and display of normative and legal documents concerning organization and performance of intelligence activity, classifiers (directories) of the state level, organizational and administrative documents, documents of regime rules and restrictions on intelligence activity are considered. The main tasks of the automated system of normative and legal support of intelligence activity according to different directions are considered. The article also determines some defined roles of specialists (officials) of the automated regulatory support of intelligence activities, as well as the issues of system architecture and main databases. A generalized organizational and functional structure of the automated system of normative and legal support of intelligence activity, which describes the automated functions of the system, is provided. Figs.: 4. Refs.: 45 titles.



UDC
621.771.23-413.004.12

Competitiveness of Ukrainian metal in the world market is stipulated by high technical requirements for its quality in general, including its mechanical properties. Introduction of effective systems of automated control of the mechanical properties of heavy-plate mills will significantly improve their quality. The article describes the formulation of the problem of controlling mechanical properties of heavy-plate rolled products, and mathematical models for forecasting their mechanical properties. The main technical solutions are implemented into the automated control system of mechanical properties of rolled products. The developed system of automated control of their mechanical properties is included into the APCS of heavy-plate mills rolling, as well as the software and hardware for this complex system is partially common to both components. APCS of the rolling process is functionally combined with the control system of the mechanical properties of rolled products. Five programmable controllers built on a PC, as well as monitors, a corresponding keyboard and printers are used to control these properties. For the organization of the automated system of control and management of mechanical properties there is used a «manual» organizational and technical structure. To test the developed system and its algorithms, there was created a laboratory installation which allowed to perform simulation of the automated control system of the mechanical properties of rolled products on the basis of a PC. During the simulation there was used experimental data from a real technological object and confirmed the operability of the obtained scientific and technical solutions. Stated above solutions to control the mechanical properties of rolled products can be used in the development of the APCS of heavy-plate mills. Refs.: 7 titles.


UDC 004.4, 004.6, 004.021

The issue of product safety is acute in many countries and companies. Indeed, every year a large number of people catch various diseases after using products contaminated with harmful substances. To increase food safety, there should be implemented some technologies which would enable quick testing of products and, using the obtained knowledge, to prevent appearance of harmful substances. Biosensor technologies which are utilized for conducting quick tests for agricultural purposes are being nowadays actively developed in the world. The use of data mining technologies can provide the identification of new knowledge about the nature and dependence of various harmful substances on external factors. The article considers the issues of construction and testing of forecasting technology, including analysis of existing solutions, search for forecasting models, usage of Data Mining methods to find qualitatively new knowledge and hypotheses, and hypothesis testing as well. The first section of the article provides an overview of existing models and methods, formulas for calculating the risk of aflatoxin. The second section contains a brief description of the data collection system which consists of a data warehouse, sensors and a mobile application as a data source. The results of data mining obtained after the use of Data Mining methods are presented in the third section of the paper. As a result, there was obtained a hypothesis of the effect on the appearance of mycotoxins in crops. Confirmation or refutation of the hypothesis was performed by testing it using OLAP-technologies. The results of the hypothesis test are presented in the last section. The main result of the work was obtaining a data analysis system ready for testing in real conditions. However, it should be noted that there is a need for more extensive testing on large amounts of data which can be accumulated over several years of observations. Figs.: 5. Refs.: 8 titles.



UDC
519.17:004.942

The article considers the method for describing program modeling where predicates are used to create a model in the form of a nondeterministic finite automaton. A format of the description of predicates with the division of their semantic and conditional parts is offered in the paper. Arithmetic operators, parentheses, standard functions, as well as temporal logic operators U and N should be used to describe the content of the predicate. For the logical part of predicates, in addition to their logical functions, it is proposed to use relation operations, arithmetic operators, parentheses and standard functions. The formation of the description of each state of the program automaton model should be completed by dividing into different branches of the model. To describe the models of parallel programs, the following special states have been introduced: a state-monitor for the access of various processes to shared resources and a state-protocol for the description of independent parallel branches. The model is created in the process of its description, so it does not require further verification. If the description of the model is performed correctly and the optimal algorithm of the future program is selected, such model will fully correspond to its description. Unlike MODEL CHECKING technology, which requires verification, it eliminates the need for model verification. The graph of the obtained model is processed by its sequential traversal on all branches with returns to the previous states and subsequent software implementation. Consecutive traversing should be performed for each branch of the model either to its final state or to the state that has already been processed during the traversal. Model processing includes transmission of the model description into an internal representation for subsequent conversion into a program in the target procedural programming language. In this case all actions in the substantive parts of the predicates, as well as the conditions of the branches in the process of transmission are converted into an internal representation of the program. This technology provides a direct conversion of the description of the program model into the program itself. Figs.: 5. Refs.: 4 titles.


UDC 004.9:004.02:630.181

Deforestation is one of the biggest ecological challenges faced globally nowadays. From 1993 to 2020 the world lost almost 154 Mha of forests which brought about various negative consequences, such as an increase in greenhouse gas emissions, disruption of water cycles, increased soil erosion, disrupted livelihoods, etc. Scientists agree that artificial forestation is the only way to solve the problem on its present scale. Classic methods of artificial forestation include manual and automated ones or their combination. Despite its simplicity and comparably easier improvement, classic methods also have some disadvantages that do not allow them to solve the problem, i.e., bad scalability. Automated forestation that utilizes UAVs is a new promising approach that was developed in the last decades. The current paper addresses its common implementations compared to classic forestation methods from the perspective of its improvement possibility based on their synthesis. Analysis of the existing experience of UAV-based forestation consists of three stages: surface scanning, data processing and planting itself. The research showed that in addition to the usage of modelling and optimization algorithms at the first two stages, analogically to classic methods higher efficiency can be achieved by planting seedlings instead of seeds. The present paper suggests performing planting from the air to the defined points based on the creation and optimization of a tree situation model. Such approach requires the usage of advanced LIDAR generated land surface modelling techniques and methods of trajectory calculation. The article describes a step-by-step new method of tree planting automation, suggesting theoretical and practical perspectives and directions for future research. Fig.: 1. Refs.: 18 titles.


 QUALITY, RELIABILITY AND CERTIFICATION OF COMPUTER TECHNIQUE AND SOFTWARE


UDC 621.3.019:658.562

Strelnikov V.P., Strelnikov P.V. Basic provisions, requirements and initial data for the calculation of spare parts sets. Mathematical machines and systems. 2021. N 3. P. 133–137.

The ability to effectively ensure pre-specified level of reliability of the equipment, while maintaining expenditures at a minimum, is one of the foremost requirements and biggest challenges of our time. One of the key elements of the current research is to determine main characteristics of spare parts, e.g. types of spare parts sets, their respective composition, indicators of sufficiency of spare elements in spare parts sets, which allows to define the most effective and cost-saving methods of spare elements inventory management for spare parts sets. There have been analyzed some methods for developing the inventory depending on the purpose of the equipment, its maintenance and repair, as well as the requirements for the equipment reliability, including periodic and continuous stocking, periodic stocking with emergency deliveries and replenishment by level. To ensure high operational reliability of electronic equipment, maintenance and repair, extending the service life of the equipment, a support system is proposed, which includes diagnostic and repair tools, sets of spare parts, etc. In addition, the paper addresses the design of spare parts while taking into account the criteria of reliability of systems operation such as the level of sufficiency, composition and volume of spare parts, which should ensure the functioning of systems with necessary reliability indicators. The suggested methods for spare parts inventory  planning and management are based on the most adequate models of reliability that, as a result, provide a significantly more accurate forecasting of the required amount of spare parts and, consequently, a more efficient equipment spare parts inventory planning. The research suggests the main requirements and necessary input data to guarantee the accuracy of such calculations. Таbl.: 1. Fig.: 1. Refs.: 3 titles.


UDC 621.3.019.3

Fidarov T.Z. Conceptual framework of the creation of a system of high quality, safe and dependable railway transportations. Mathematical machines and systems. 2021. N 3. P. 138–148.

The paper addresses the most important problems and tasks related to the objective need to create a single service delivery system for the railway industry of Ukraine which will provide high quality, safe and reliable service for the existing types of freight and passenger traffic. There have been considered three main classes of problems connected with rail transportation: maintenance of these processes by reliable and dependable service provided through the use of technical means; functioning of the service delivery system with the help of specialized software and hardware; monitoring and adjusting the processes of providing services during their implementation. Effective use of the means of the Ukrainian railway transport network (RTN) requires an analysis of the possible risks of RT during the transportation and the use of the corresponding means to reduce the impact of risks in the transportation processes. The quality of transportation management can be significantly improved through the synthesis of these tools into a single system. It is necessary because in most cases of emergencies during transportation, such a system will collect and process statistics of emergencies to create a classification of the most dangerous ones in the form of a separate statistics. It, in its turn, will allow to objectively and promptly analyze both the causes of certain types of emergencies and accidents during transportation, and significantly reduce not only the risks of their occurrence, but also the potential damage from them. The article also offers a concept of system creation which allows to create a reliable, high quality, system-organized and practically safe system of RT services. Such a system will be a little bit dependent on the impact of most external and internal hazards and risks what is necessary to improve the quality of the provided services. For these problems there have been formulated and presented some specific examples of their solution that can be used for the provision of European quality services. Fig.: 1. Refs.: 20 titles.


 

            

       Last modified: Oct 7, 2021