APPROACH TO MATHEMATICAL MODELING OF THE DISTRIBUTION OF THE ACADEMIC LOAD OF THE TEACHING STAFF OF THE DEPARTMENT BASED ON SET THEORY
UDC 004.02; 004.942; 378.1
T.I. Kasatkina, E.V. Bolgova, L.V. Rossikhina, R.V. Kuzmenko
The purpose of the research is to develop an approach to modeling the distribution of educational load, taking into account the features and specifics of each Department and the requirements of the educational organization. The model built on the basis of this approach can be used as an auxiliary tool when compiling the load for each of the departments. The distinctive features of the proposed approach to modeling are such features as the ability to adapt the subject area, which provides the search and implementation of the optimal ratio of discipline-employee of the Department from among the teaching staff; compliance of the report structure with the requirements of the reporting documentation instructions on labor rationing of teaching staff or similar documents of departmental educational organizations; the possibility of using the model for any number of employees staff of the Department and any number of types (number of subjects) and types (classes lecture-type class-type seminars, practical classes, etc.) teaching load of the Department, as well as the possibility of changes outside the classroom and extracurricular load PPP. As research methods and criteria for optimal load distribution, we used the weight coefficients of teaching staff, depending on the type and type of educational work and the matrix of personal weight coefficients of employees. The possibility of using set theory methods in load modeling was also shown. Based on the results of the research, an approach to the representation of the academic load of the Department in the form of sets of sets is proposed. It is shown that the load distribution problem can be reduced to solving an unbalanced modeling problem. A lot of “teaching load of the Department” consisting of many “types of Cathedral work,” many “types of academic work” and many “workers of the faculty of the Department.” The structure of the set of ” types of educational work “is represented as a combination of a subset of” classroom contact work “and a subset of”extracurricular work”. A relational scheme of relations in the load distribution model and its structural units, which are sets, is proposed. The direct and feedback relationships between structural units are shown. A set of weighting factors for the level of professional competence of an employee has been developed and a method for calculating its elements has been developed. At the same time, the method of determining the level of competence of the employee of the teaching staff of the Department by type of work is clearly demonstrated in the form of diagrams. A model for implementing the optimal distribution of academic load between the teaching staff of the Department is proposed based on a comparison of the levels of competence of teaching staff in each discipline from the set of “types of Cathedral work”. As a result of research and development, an approach to the distribution of educational load was proposed, which makes it possible to present the educational load of the Department in the form of sets of sets, and allows to distribute the educational load taking into account the features and specifics of each Department of an educational organization. Calculations of employee competence levels were performed, the results of which are presented in the form of diagrams. As a result, it is concluded that the proposed approach to distribution will allow higher education organizations to significantly reduce the burden on the teaching and administrative staff of the organization, and thus make it possible to increase the time resources for making managerial decisions and performing teaching duties.
Keywords: mathematical model, educational organization, load distribution, discipline, educational load, set, report, department.
MATHEMATICAL MODEL TO DETECT ANOMALIES USING SENSITIVITY ANALYSIS APPLYING TO NEURAL NETWORK
UDC 519.25: 004.891.3
R.V. Scheglevatych, A.S. Sysoev
The transition to the digitalization in various spheres of economic and social activity is accompanied by the emergence of large amounts of data, processing which it is necessary to identify certain dependencies and build models of processes or systems. The task to identify anomaly values in dig data sets is relevant. Existing algorithms to detect anomalies are based on different approaches and have their own advantages and disadvantages. However basic schemes of all methods are similar and use at the initial stage the separation of data in a typical for system or process and those that are not, then follow structural and parametric identification of the model, and at the final stage the trained model is used to separate the data. To improve the accuracy of algorithms, they can be modified to take into account the data structure or to combine heterogeneous mathematical models. The paper describes a combined approach to build the system for detecting anomalies based on the Isolation Forest algorithm and sequential application of a neural network classifier. To reduce the dimension of neural network input vector, the approach to Sensitivity Analysis based on applying Analysis of Finite Fluctuations to the neural network model is synthesized and described. It is presented the numerical example that shows the adequacy of the proposed approach to data analysis.
Keywords: mathematical model, anomalies, sensitivity analysis, neural-network models.
THE SYSTEM OF DECISION-MAKING SUPPORT FOR OIL CONDITIONING USING BY DIGITAL TWIN OF TECHNOLOGICAL PLANT
This paper is about using of the digital twins for oil conditioning plants. A relevance of this theme is due to continuous monitoring of conditional oil quality. This problem arises when conditioning oil is the mix of low-and high H2S content streams. The main idea of this paper is theoretical calculation of the oil quality in between laboratory analyses. This task is colving using by mathematical modeling of the oil conditioning plant. A foundation of model is the Peng-Robinson cubic equction of state. The proposed digital twin is realized by Russian program «MiRPiA Process». In the considered case a composition of source oil changes dynamically. The mathematical model predicts rates and compositions of the conditioned oil and a gas condensate. Therefore digital twin allows to determine parameters of an exploitation mode: last separation temperature and rate of H2S neutralizer. This paper may be interesting for oil conditioning specialists.
Keywords: digital twin, oil conditioning plant, mathematical model, saturated vapor pressure, removing H2S from oil.
DEVELOPMENT OF A MATHEMATICAL MODEL OF THE PROCESS OF PROVIDING HIDDEN INFORMATION EXCHANGE IN RADIO SECURITY SYSTEMS AND A COMPUTATIONAL METHOD FOR ASSESSING THE STEALTH FOR THEM
To control large areas, radio security systems are currently being used that provide information collection from radio-distributed sensors distributed throughout the facility. When a person or a foreign object enters the sensor’s coverage area, the sensor detects the occurrence of an emergency and sends an alarm signal via radio channel to the system control panel. At the same time, it is known from the literature that radio security systems themselves are subject to destructive influences aimed at disrupting their performance. In this work, the author, based on the previously proposed mathematical model and generalization of the known literature, developed a mathematical model of the process of providing hidden information exchange in radio security systems, taking into account the destabilizing effects (for example, imposing false data or suppressing interference) on the transmitted signals in the communication channel. A computational method has also been developed for assessing the stealth of information exchange in radio security systems based on fuzzy logic, the use of which under conditions of poorly structured and difficult formalizability of the source data and also in the conditions of a complex of destructive influences, can potentially help to more adequately assess the stealth of radio security systems. The results can be used to study the stealth of known and promising radio security systems. It is also possible to use the results obtained to increase the stealth of known and promising radio security systems.
Keywords: mathematical model, computational method, stealth, radio channel, radio security systems.
TWO-DIMENSIONAL MODEL OF STATIONARY TRANSFER OF BINARY ELECTROLYTE IN GALVANOSTATIC MODE
A.M. Uzdenova, M.Kh. Urtenov, N.O. Chubyr, A.V. Kovalenko
In electromembrane systems, the transfer of the binary electrolyte in the stationary case may be realized either in potentiostatic (PSR) (given the potential drop, ) or in galvanostatic (GSR) modes (given the average current density, ). These modes are alternative to each other. At theoretical and experimental researches it is convenient to work in GSR. However, the system of Nernst-Planck-Poisson equations (NPP) is convenient for simulating transfer in the PSR, but inconvenient for simulating in the GSR, due to the lack of an equation for the current density. Using the method of mathematical transformations from the original system of equations of the NPP transfer model to the PSR, a system of equations modeling the transfer to the GSR is obtained. The numerical analysis is given using finite element methods. In work: a new equation for the current density is obtained from the NPP by transformations; the boundary conditions required to determine the current density are derived; an algorithm for calculating the current-voltage characteristic is developed. We performed a numerical analysis of the boundary value problem and showed that there is a complete correspondence between the current-voltage characteristics (CVC) calculated in the PSR and GSR at pre-limit densities and a slight difference at exorbitant current densities. This shows the adequacy of the proposed mathematical model of transfer in galvanostatic mode and the algorithm for calculating the CVC. The paper proposes a model of transfer in the GSR, numerical analysis of the boundary value problem and shows that there is a complete correspondence between the CVC calculated in the PSR and GSR at pre-limit densities and a slight difference at exorbitant current densities. This confirms the adequacy of the proposed mathematical model of transfer in the galvanostatic mode and the algorithm for calculating the CVC. The proposed model of GSR transfer can serve as a mathematical tool for processing the results of experimental studies of GSR transfer.
Keywords: numerical methods, membrane systems, ion exchange membrane, galvanostatic mode, potentiostatic mode, mathematical model.
MODEL OF PRODUCTION QUALITY CONTROL AND PREDICTION UNDER THE CONDITIONS OF A POTENTIALLY HAZARDOUS AUTOMOBILE TIRE VULCANIZATION PROCESS
B. Yahiaoui, A.A. Mitrokhin, V.L. Burkovsky
Quality of products is one of the most important criteria of efficiency of any production. Control systems of potentially dangerous technological processes should be subject to constant development and improvement in connection with the indisputable importance of ensuring proper quality control, as potentially dangerous technological processes are complex formalized systems that operate under conditions of uncertainty, incomplete knowledge and fuzzy descriptions of both the system itself and the signals acting on it. In this paper, a potentially hazardous technological process of vulcanizing automobile tires is considered a subject of study. The paper presents a generalized structure of the control object, as well as a mathematical model of the control object, organized in the form of a set of values that describe the processes in the real system, analyzes the parameters that affect product quality. In order to improve the quality of the final product, a model for controlling and predicting the functioning of a dangerous technological process of vulcanization is proposed. The paper presents a generalized structure of the control model and the prediction of the quality of the finished product, the implementation of the model in relation to the vulcanization process.
Keywords: potentially dangerous objects, mathematical model, technological process, vulcanization.
FORMALIZATION OF THE ACCESS CONTROL AUDIT PROCEDURE IN THE INFORMATION SYSTEM
The article discusses current problems and tools for ensuring information security in information systems. The author analyzes the current trends in information security breaches in 2018-2019, concludes about the relevance of countering threats related to unauthorized access. The basic tools for protecting an information system from unauthorized access are many rights and rules for access control between objects and subjects. Therefore, to ensure the necessary level of security, the adequacy and consistency of the distribution of access rights is important. The methodology and conceptual scheme for conducting an audit of the access control subsystem based on ACL lists, consisting of procedures for initiating audits, collecting and analyzing audit data has been developed. The mathematically model of audit procedure is automation in the form of an audit software tool for the access control subsystem using the Windows operating system as an example. The main advantage of the proposed audit procedure is that it does not require complex testing procedures, calculation of probabilities, involvement and selection of experts. The main purpose of the program is to assess the compliance of the existing settings of the access control policy in the system with the security policy of the system under investigation.
Keywords: access rights, information protection, operating system, access control model, mathematical model, cybersecurity.
PREDICTION OF THE CONSEQUENCES OF THE PROPAGATION OF THE VIRUS IN A COMPUTER NETWORK USING A BASIC REPRODUCTION NUMBER
Today, Internet is considered to be one of the most useful tools for people to communicate, find information and to buy goods and services. Most computers are connected to each other in some way. The Internet is the primary medium used by attackers to commit computer crimes. They share the same operating system software and communicate with all other computers using the standard set of protocols. This has spawned a new generation of criminals. The similarity between the spread of a biological virus and worm propagation encourages researchers to adopt an epidemic model to the network environment. This approach is most effective for describing the computer viruses propagation on the network. The article uses the results of the theory of mathematical epidemiology to analyze the SIRS model. The dynamics of the virus propagation to the computer network is described using a system of differential equations. The stability of the network to the spread of malware is investigated. An equilibrium position is found. The basic reproduction number is determined. The dependence of the virus attack evolution on the basic reproduction number is analyzed. Numerical simulations are provided to support our theoretical conclusions.
Keywords: mathematical model, computer virus, virus dynamics, basic reproduction number, nonlinear system of differential equations, stability of the system.
MATHEMATICAL MODEL TO ASSESS THE INFLUENCE OF ELECTROMAGNETIC FIELDS ON THE EMERGENCE AND DEVELOPMENT OF OCCUPATIONAL DISEASES IN THE ELECTRICITY SECTOR
M. A. Myasoedova, N. A. Korenevskiy, L. V. Starodubtseva,
M. V. Pisarev
The aim of the study is to develop mathematical models for assessing the impact of electromagnetic fields of different modality and intensity on the human body providing a solution to the problems of assessing the health of people employed in the electric power industry with acceptable accuracy for medical practice.The technology of soft computing and, in particular, is chosen as the basic mathematical apparatus, the methodology of synthesis of hybrid fuzzy decision models developed in the South-West state University has proven itself in the synthesis of mathematical models of forecasting, early and differential diagnosis of diseases with a similar structure of the studied classes of States. As an example, a mathematical model for predicting the appearance and development of immune system diseases in employees of electric power enterprises of the Kursk region is described. Fuzzy mathematical models use membership functions with basic variables that take into account the intensity of the electromagnetic field of industrial frequency, work experience in the power industry and individual risk factors that provoke the appearance and development of diseases of the nervous system. In the course of mathematical modeling and expert evaluation it was shown that the use of the chosen methodology of synthesis of hybrid fuzzy mathematical models allowed to obtain a mathematical model of forecasting and development of diseases of the immune system in employees of the electric power complex with confidence exceeding 0.9.
Keywords: :mathematical model, fuzzy logic, occupational diseases, immune system, power engineering, forecasting
A MATHEMATICAL MODEL OF THE ASSESSMENT OF THE SEVERITY OF GENITAL HERPES ON THE BASIS OF FUZZY LOGIC
M.I. Lukashov, E.V Pismennaya, O.Y. Olisova, L.V. Starodubtseva, L.V. Shulga
The work is devoted to the urgent problem of improving the quality of medical care for the population suffering from genital herpes due to the timely and qualitative assessment of the severity of the disease under study. In the course of the research, a fuzzy mathematical model was obtained, which allows to distinguish four classes of patient’s conditions: patients with clinically undetectable genital herpes; patients with detected traces of herpes; patients with detected herpes; patients with clinically observed herpes. The methodology used in the synthesis of hybrid fuzzy decision rules allows to reliably separate the selected classes of States in the conditions of incomplete and fuzzy representation of the original data with a strongly overlapping structure of classes. The chosen classification system allows to rationalize the choice of treatment regimens depending on the individual condition of patients. As a result of the research it was found that the use of fuzzy logic of decision-making, can improve the quality of decision-making, according to the stages of disease by 10,…, 15% and reduce the duration of treatment by 5,…10%, which allows us to recommend the results for use in medical practice.
Keywords: : mathematical model, genital herpes, fuzzy logic of decision – making, laboratory indicators.