Mathematical Machines and Systems. 2024 #2

ABSTRACTS


COMPUTER SYSTEMS

UDC 681.3

The article is devoted to a review of the historical development of computer technologies and their application in various spheres of life in modern society. The evolution of computing technology (from the first bulky electronic computers to modern computers and promising quantum systems) is studied in detail. Special attention is paid to the formation and development of artificial intelligence, machine learning, and big data technologies, which led to a revolution in computer science and opened new opportunities for automation and efficiency improvement in many industries. By analyzing current advances in AI, machine learning, and cybersecurity, the paper identifies some changes in the development of computing technologies and envisions their potential for future breakthroughs. In addition, the article predicts further developments in computing and information technology, as well as related ethical and social issues. Special attention is paid to ensuring the impact of artificial intelligence and robotics in the military sphere. The paper analyzes the use of combat robots, unmanned aerial vehicles, and other autonomous systems in modern armed conflicts, as well as some trends in the development of technologies for joint actions of combined groups of drones. The use of AI systems in situation centers and decision-making processes is considered. The last part of the paper is devoted to the consideration of the possibility of applying generative models based on transformers, such as GPT, in situation centers and decision support. It reveals how these technologies can be used for automated analytics, text generation, and the creation of intelligent assistants that can significantly improve the performance of information systems. The article concludes by defining the key role of computer technologies in the modern world and the need for comprehensive regulation of management processes, taking into account not only technical but also ethical and social aspects. In general, the article presents a comprehensive analysis of the history and current state of computer technologies, as well as their activities in various spheres of society. The achievements in this field are described, and the phenomena and trends of interest to specialists in the fields of information technology, system analytics, and management are identified. Figs.: 21. Refs.: 19 titles.


UDC 004.89

The development of neural networks began in the 1940s, when scientists began to model the nervous system. However, the real breakthrough occurred in the 2010s with the advancement of machine learning and deep learning. Digitalization, Big Data, and the ability to process large datasets have created a powerful resource for machine learning. By utilizing large amounts of data and powerful computational resources, neural networks have become able to achieve incredible results in such areas as computer vision for object recognition, natural language processing, medicine, forecasting, pattern recognition, autonomous vehicles, etc. A neural network is a mathematical model that describes the interdependencies between different factors with mathematical formulas and allows for discovering patterns and dependencies between input data and the final result during training. After training, such a neural network can be used to predict outcomes. The article discusses the principles of neural network operation, the architectures of their mathematical models, the security and challenges of neural networks, modern products based on neural networks, and their practical applications. Neural networks are a modern, powerful tool of artificial intelligence capable of modeling and simulating the operation of the human brain. Machine learning and neural networks have been integrated into information technology for many years. One of the leaders in their development is IBM, which was one of the first companies to implement machine learning technologies, based on which IBM Watson operates. A real sensation was the ChatGPT neural network, a language model that generates text based on user queries, taking into account the context of previous queries. Therefore, neural networks are capable of learning based on large volumes of data and recognizing complex dependencies in them, so they are used to solve complex problems that cannot always be solved using mathematical formulas or rules. Figs.: 6. Refs.: 10 titles.


UDC 623.764

Sapaty P.S. Networking Solutions in Combined Distributed Worlds. Mathematical machines and systems. 2024. N 2. P. 33–48. 

The paper analyzes the rapidly growing importance of graph and network models and tools in such areas as transport, communications, social and military systems, goods production and distribution, education, economy, biology, psychology, criminology, climate change, etc. It aims at the development of effective methods capable of integrating different types of networks into higher-level infrastructures representing advanced social systems, particularly considering the symbiosis of goods production, goods evaluation, and the obtained product delivery systems under some universal networking concept. In a search for the latter, the article briefs the developed and patented Spatial Grasp Model and Technology (SGT) with its basic Spatial Grasp Language (SGL), which allow for fully distributed and parallel operations on arbitrary large and complex networked structures. The paper first shows some elementary networking operations in SGL useful for a better understanding of the rest of the material. Then it provides several practical examples of combined networking solutions, which include scenarios in SGL for finding the strongest production centers in their networks, as well as the most powerful user communities interested in and requesting particular types of products. After the selection of specific producers and consumers, the paper forms a distributed virtual and physical delivery infrastructure oriented on all of them and based on the shortest paths from producers to consumers and shows live the distribution process in SGL. The obtained results confirm that the deep integration of heterogeneous distributed systems can be organized naturally and automatically within the global integrity, awareness, and consciousness processes under the Spatial Grasp paradigm, as was already discussed in the previous publications on SGT. Figs.: 11. Refs.: 93 titles.


       INFORMATION AND TELECOMMUNICATION TECHNOLOGY

UDC 004.65:681.5

Smolij V.M., Kovalenko O.Ye., Smolij N.V. Information model for supporting the process of electronic devices production. Mathematical machines and systems. 2024. N 2. P. 49–64. 

The process of the production of electronic devices was considered as an interaction of ERP-, MES-, and PDM-subsystems, which made it possible to find some directions and levers of influence on the acceleration of the production process, customization for specific technological solutions, and available warehouse stocks. The tasks of the need for a more detailed analysis of the connections between the specified subsystems by studying the interaction and modeling the management process using the example of database queries were defined. A scheme for forming orders for production was proposed, namely, the need for electronic devices of a certain configuration and parameters should be monitored, its satisfaction by organizing production; acquisition (re-equipment, modification) of components, creation of a model and direct production; inspection and acceptance tests with the provision of relevant documents and supplies to fulfill the direct appointment by electronic device. Special attention was paid to the organization of the production of electronic devices in modern military realities to speed up the production process with the provision of customization to the specific technical requirements of an individual customer and simultaneous consideration of the available stocks of components in the warehouse and those that satisfy the relevant technical characteristics of the finished device. The selected subject area was studied and the description of the subject area, input and output data was made. Designing the database was carried out by building an infological model of the database, normalizing tables in the design of the database, and developing a datological model of the database. The infological model of the database includes the description of entities, attributes, interrelations, and the «entity-relationship» diagram. Databases were created by filling the database with values and improving work with equipment, orders, and clients. The organization of the data sample from the database was analyzed, namely, the data samples, the sample of calculated values, and the sample using templates were evaluated, the grouping of data during the organization of queries was carried out, and the tables were combined. Tabl.: 5. Figs.: 7. Refs.: 23 titles.


UDC 004.8

Kamak M.D., Kazymyr V.V., Kamak D.O. Method of detection the quadcopters and octocopters based on YOLOv8 model. Mathematical machines and systems. 2024. N 2. P. 65–77.

The relevance of the topic of the article is determined by the growing prevalence of unmanned aerial vehicles (UAVs) not only in the civilian but also in the military field, where they create significant problems for air defense. The paper presents a practical test of the possibility and effectiveness of using the YOLOv8 model for detecting quadcopters and octocopters in video streams, which is designed for real-time object detection and image segmentation. A training method is used that adapts the YOLOv8 model by applying a «transfer learning» approach to adjust pre-trained YOLOv8 weights to drone-specific data. The ability of the model to work effectively in various environmental conditions is investigated, too. The conducted experiments demonstrate the efficiency of the developed method to accurately identify UAVs in various situations, which makes it important for improving aerial surveillance tools and security mechanisms. The study also explores the model’s adaptability to changing observation conditions, ensuring its robustness in processing images and video. The results indicate the high potential of the YOLOv8 model in enhancing the capabilities of air defense systems and bolstering security measures against UAV threats. Additionally, the article discusses the computational efficiency of the model, highlighting its ability to process video streams in real time with minimal computational resources. The precision and recall metrics of the model are evaluated, demonstrating its ability to accurately detect UAVs while minimizing false positives. Overall, the findings underscore the importance of leveraging advanced machine-learning techniques for effective UAV detection. Таbl.: 1. Figs.: 11. Refs.: 15 titles.


                                    
                              SIMULATION AND MANAGEMENT

UDC 519.61:621.3

It is generally accepted that the proximity of the matrix to degeneracy uniquely determines the instability of the system of linear algebraic equations (SLAE). There is only an assumption that the instability of the numerical solution of the SLAE in the case of a matrix close to degeneracy is caused by the rounding error of the arithmetic operation of addition (subtraction). When determining the mechanism of the interrelation of the matrix close to degeneracy and the solvability of the SLAE, as a model example, all stages of the calculation of the electric circuit are analyzed, namely, the description of the graph of the linear electric circuit, the composition of the SLAE describing the circuit, and the solution of the complex system. For the first time, it was proposed to use the conductivity of the bipolar component located between the nodes of the electric circuit graph as an indicator of the matrix close to degeneracy. The dependence of the accuracy of the SLAE solution on the value of the conductivity of the indicator component was calculated for two variants of the voltage and conductivity of the indicator component in the SLAE. The analysis of the calculation results showed for the first time that the rounding error of the arithmetic operation of addition (subtraction) leads to the loss of accuracy or instability of the numerical solution of the SLAE with the matrix close to degeneracy. The influence of the error on the computational process of the numerical solution of the system was performed in two stages. For the first time, it was established that the interrelation between the matrix close to degeneracy and the stability of the SLAE solution depends on the selection of the voltage of the indicator component in the vector of SLAR variables at the stage of compiling the equations describing the electrical circuit. The interrelation exists if the voltage of the indicator component is not included in the vector of variables and does not exist if the voltage of the indicator component is included in the vector of variables because the second rounding error operation stage does not work. An algorithm for selecting the variables of the SLAE, which is composed, is proposed to obtain a stable solution for the system. Tabl.: 2. Fig.: 1. Refs.: 4 titles.


UDC 004.5

The task of adapting complex (organizational) systems in the process of their functioning is becoming increasingly relevant as computing tools and means of communication develop. At present, it is not yet possible to say that the goal of constructing a formal method for managing adaptation processes has been fully achieved. From the analysis of scientific literature, it follows that the results presented to date on adaptation methods and models do not yet allow solving large-scale problems. However, it is with this dimension of systems that we have to deal with when solving practical problems. To a large extent, adaptation methods represent expert approaches and procedures for preliminary analytical study. The central task of adaptation methods is the task of synthesizing a structure with given properties. Currently known results on this topic use an ontological approach and algorithms based on the theory of systems algebra, stages of sets, and conceptual design. The article discusses the methodology of set-theoretic and algebraic synthesis of topologies in the form of tensor transformations of electrical networks by G. Kron as an alternative to existing approaches to the synthesis of structures. Based on tensor transformations, it is possible to construct formal methods for transforming the structures of organizational systems, provided that they are correctly interpreted in terms of electrical networks. A variant of establishing a correspondence between the parameters of electrical networks and the quantitative characteristics of organizational measures is presented. As an example illustrating this correspondence, a system of educational institutions for training specialists for the economic sector is given, which is interpreted as a «nodal» multi-coil electrical network with cross-connections between coils. Such parameters of the electrical network as current strength and potential difference in individual coils, their admittances and admittances of cross-connections of the network are matched with expressions for the beneficial effect, financial costs, and indicators of useful output, taking into account the mutual influence of educational institutions. An expression for the transformation tensor is obtained and the sequence of calculations when transforming the structure of the specialist training system with subsequent assessment of its characteristics is shown. Figs.: 5. Refs.: 12 titles.


UDC 504.064.3

The present study is devoted to solving problems related to the optimal choice of a rational carrier based on an unmanned aerial vehicle (UAV) and, accordingly, special equipment for performing remote radiation reconnaissance and monitoring of complex radiation contamination of the area. The relevance of the research arises from the need for a prompt response to the risks associated with the possible use of tactical nuclear weapons and accidents (destructions) of nuclear facilities (nuclear power plants, nuclear waste repositories, radioactive waste storage facilities, etc.) caused by the aggressive actions of pariah countries (Russia, North Korea, Iran) in the world. Such threats require prompt assessment of the levels of contamination in the areas where troops (military) and the civilian population are located, to ensure the awareness of officials in order to make appropriate decisions by military administration bodies. The article analyzes the subject area of using unmanned dosimetry systems (UDS) and describes a step-by-step systematic approach to determining a comprehensive indicator of the effectiveness of their use. The mathematical formalization of the stages of a systematic approach to equipping UDS according to the relevant groups of factors is substantiated. The following methods have been developed: 1) a comprehensive, step-by-step analysis of UDS configuration options based on group expert assessment; 2) a comprehensive analysis of UDS configuration options based on multi-criteria optimization and, on its basis, an algorithm for selecting configuration options was developed. This makes it possible to select a rational type of UAV and a set of special equipment for unmanned aerial systems for remote radiation reconnaissance in accordance with the decision-making official of the Armed Forces of Ukraine. Tabl.: 4. Figs.: 3. Refs.: 16 titles.


 QUALITY,  RELIABILITY, AND CERTIFICATION OFCOMPUTER                                          TECHNIQUE AND SOFTWARE

 UDC 620.169.1

Fedukhin O.V., Cespedes Garcia P.D. Determining residual product life considering multiple degradation processes and variable loading. Mathematical machines and systems. 2024. N 2. P. 126–137.

As of today, significant progress has been observed in the field related to the analysis of various types of degradation processes occurring in technical elements and systems. In most studies, each of these processes is examined individually, and the comprehensive assessment of the impact of all degradation processes on the final residual life value is limited by considering a single dominant process the one that develops most intensively, known in reliability theory as «the weakest link». Applying this method simplifies the overall degradation profile significantly and contributes to an overestimation in the final prediction which is unacceptable in critical application systems. The article proposes an approach that, in an accessible engineering form, allows for the necessary calculations to assess the residual life of a product that is simultaneously under the influence of multiple degradation processes with varying degrees of participation and temperature loads. This approach relies on calculating the mean rate and coefficient of variation for the generalized degradation process. The calculations are conducted employing a probabilistic-physical approach, within which lies a probability model in the form of a diffusion monotonic failure distribution (DM-distribution). This distribution is presented with the involvement of a Markov diffusion-type random process with a constant speed which properly adapts and aligns statistical failure data of mechanical objects. Being influenced by multiple degradation processes, the normalization of the initial data and information regarding the proportions of each of the components in the general degradation process has been used for the first time. The application of this approach allows for a more accurate estimation of the product’s residual life compared to the estimation obtained by considering only one dominant degradation process. The detailed assessment of the residual life, which is obtained after refinements, contributes to reducing operational costs through the optimization of technical maintenance intervals and establishing the actual service life of the researched objects. Tabl.: 2. Figs.: 2. Refs.: 8 titles.


 

 

            

       Last modified: Jul 9, 2024