ESTIMATION OF PAIR LINEAR REGRESSION MODELS WITH PARAMETERS IN THE FORM OF LINEAR OPERATOR MATRICES OF TWO-DIMENSIONAL VECTOR SPACE
M.P. Bazilevskiy, L.N. Vlasenko
The key problem in constructing a regression model is the choice of its structural specification, i.e. the composition of the variables and the mathematical form of the relationship between them. All currently known regression specifications are based on the fact that their unknown parameters are matrices of linear operators of a one-dimensional vector space. In this paper, for the first time, linear regression models with parameters in the form of matrices of linear operators of a two-dimensional vector space are considered. It is shown that such models can be used to predict the values of the explained variable, and for this, the researcher does not need to set the predicted values of the explanatory variable, since they are sequentially determined by the model. To estimate the proposed models, an optimization problem is formulated based on the least-squares method with restrictions. Using the method of Lagrange multipliers, it is proved that solving the formulated problem reduces to solving linear algebraic equations system. An example of estimating the proposed models for specific data is considered. As a result, the error sum of squares by the developed model turned out to be five times less than the error sum of squares by the classical pair linear regression model.
Keywords: regression model, linear operator, vector space, forecasting, ordinary least squares, method of Lagrange multipliers.
FORECASTING TIME SERIES USING EVENT BINDING
This article discusses the concept of modification of the time series analysis method, focused on integration with clustering methods in real-time training mode. Various methods of forecasting time series and machine learning are analyzed. The method described in the article predicts the behavior of the time series based on large data obtained from various sources and associated with existing transactions in the time series. This approach makes it possible to find the dependence of changes in certain indicators of the considered systems depending on various events. The performed research offers the concept of automated system training in real time with the possibility of further software implementation. The concept under consideration allows you to build forecasts for any time series, depending on various events, news and data that are in the public domain. An approach is proposed that links events to a transaction chart. The advantage of this approach is the ability to find various dependencies between events and various changes in indicators, for example: prices on exchanges, values of social indicators and many others.
Keywords: data analysis, forecasting, time series, big data, cluster analysis, data mining.
FORECASTING OF MANIPULATIVE INFORMATION INFLUENCES
IN SOCIAL NETWORKS: TERRITORIAL ASPECT
V.A. Minaev, K.M. Bondar, E.V. Vaits, A.V. Kantysheva
Negative factors affecting information security of countries are described. Special attention is paid to the information-psychological effects highlighted in the Doctrine of information security of the Russian Federation. It is pointed to the expansion of the use of simulation methods for modeling information impacts on social groups and the corresponding information counteraction. The necessary definitions related to the use of the simulation approach proposed for the study of complex nonlinear systems to the modeling of information influences in social networks are given. The description of the system-dynamic model of information counteraction in the form of differential equations system is given. Simulation experiments were carried out with the model on the Anylogic software platform and analytical dependences of characteristic times reflecting the susceptibility of the population of the country’s settlements to influence through social networks, including mechanisms of negative influence, on the statistical characteristics of users were obtained. Typology of settlements of the Russian Federation on characteristics of information propagation in social networks of regions is carried out. It is concluded that the identified relationships can be used to predict manipulative information effects and planning information counteraction. In addition, it is emphasized that the simulation model allows, using statistically observed variables, to estimate parameters and variables characterizing the dynamics of information propagation in the population, which are statistically unobservable.
Keywords: simulation model, information manipulative influence, forecasting, counteraction, social network, typology, cluster analysis.
MULTI-METHOD APPROACH TO THE MODELING OF COMPLEX SYSTEMS BASED ON MONITORING DATA ANALYSIS
Y.E. Lvovich, A.V. Pitolin, G.P. Sapozhnikov
The article justifies the necessity of building various classes of mathematical models of complex systems as well as the relevance of a multi-method approach to the processing and modeling of monitoring and rating information, due to the variety of management tasks and resource efficiency optimization management of a non-profit educational organization in combination with rating management. The starting points are tentatively reduced sets of input indicators influencing the output indicators of a management unit functioning. It is based on time series forecasting on the base of additive and elementary functions. The dependence of the output performance on the input ones is determined by the regression model with the inclusion of time variables. The transition from a regression model to a neural network model is carried out, to improve the accuracy of forecasting for the purpose of managerial decision making at a certain planning horizon. The transformation procedure of initial time series into statistical samples of their prognostic estimates followed by randomized training sample development is proposed. The paper also demonstrates that the multi-method approach to the modelling provides a solution to a number of tasks concerning complex systems resource efficiency management.
Keywords: forecasting, modeling, management, resource efficiency, randomization
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
SOFTWARE IMPLEMENTATION INTELLIGENT SYSTEMS DECISION-MAKING WHEN MANAGING NUCLEAR ENERGY FACILITIES
UDC 004: 681.5
V. P. Povarov
The work is devoted to the development of the software complex of the intellectual decision-making system in the problems of management of the processes of functioning of nuclear power facilities. It is shown that the construction of the software complex requires the choice of structure based on the analysis of the tasks assigned to the software. Taking into account the developed mathematical software, implemented in the form of a set of mathematical models that allow to analyze data by processing the input information, and algorithms that perform the formation of the system structure, its optimization and ensure its operation, the following main functions were identified and implemented: the formation of a regression model depending on the input information flow of informative data; the formation of a neural network structure depending on the input information flow of data; configuration of system parameters in order to ensure the required quality of its functioning; visual display of information about the quality of the software; providing data storage in an accessible and easy to understand form; providing storage of configurable system parameters and their dynamics in the learning process ANFIS-like neural network model. The proposed engineering solutions have improved the quality of decision-making due to the efficiency and reliability of the processed information, as well as by reducing the overall error of the forecast.
Keywords: :decision-making system, multiparameter monitoring, forecasting, database, knowledge base, fuzzy neural network.
MATHEMATICAL MODELS FOR PREDICTION AND EARLY DIAGNOSIS OF DISEASES OF THE NERVOUS SYSTEM PROVOKED BY CONTACTS WITH TOXIC CHEMICALS
L.V. Starodubtseva, R.V. Stepashov, L.P. Lazurina, R.A. Krupchatnikov,
The work is devoted to the urgent problem of improving the quality of medical care to workers in contact with toxic chemicals in the process of their production or during the production process. In the course of studies, it was shown that contact with toxic chemicals causes a range of diseases among which occupy a significant place disease of the nervous system. One of the ways to combat this class of diseases is timely and qualitative prognosis and early diagnosis allows to prescribe adequate schemes of prevention and treatment. Taking into account the multiplicative and prolonged effect of toxтв ic chemicals on the human body, as well as the heterogeneity and fuzziness of the description of the studied classes of States for the synthesis of the relevant decision rules, the methodology of synthesis of hybrid fuzzy decision rules developed at the Department of biomedical engineering of Southwestern state University was used. In the course of application of this methodology mathematical models of forecasting of emergence of diseases of nervous system with the reliable three-year forecast and diagnostics of early stages of this class of diseases were received. In the course of statistical tests on representative control samples, it was shown that the confidence in the decisions made exceeds 0.85. Practical applications of the proposed method and models will improve the quality of medical services to employees of the agro-industrial complex by increasing the working age and reducing disability.
Keywords: : models, forecasting, early diagnostics, diseases, nervous system, toxic chemicals.
A SOFTWARE APPLICATION FOR THE ANALYSIS OF PHASE TRAJECTORY OF DYNAMIC SYSTEM WITH USING OF QUALITATIVE THEORY OF DYNAMICAL SYSTEMS(ON EXAMPLE OF THE ORGANIZATION IN THE MANAGEMENT OF HOUSING AND COMMUNAL SERVICES)
UDC 519.688: 332.87
А.А. Popov, А.О. Kuzmina
The purpose of the article is the enhancement of the instruments for automation of the qualitative research of the dynamic system and forecasting values of the parameters, which characterize organization activities in the economy (particularly in the field of management of housing and communal services). In this article, the problem of automation of the analysis of the phase trajectory of the dynamic system is solved (organization of management of housing and communal services), using the qualitative theory of dynamic systems. The research is relevant due to the insufficient level of automation of qualitative research of dynamic systems in the economy with the economic interpretation of research results. Methods of qualitative theory of dynamic systems, which are used, allow forecasting the state of the dynamic system without numerical simulation (for example, integrating differential system, which is a model of the dynamic system). In the article is presented technique, in accordance with research of the phase trajectory of the dynamic system using the software application, was conducted. Types of phase points in the phase plane in accordance with character of behavior of the phase trajectory plane in the neighborhood of the projection of the phase point were identified. By the example of the phase trajectory analysis, which characterizes activity of organization of management of housing and communal services, opportunities of the software application, building of projection of the phase trajectory into the three planes occurs. It was identified that in the phase planes equilibrium states as «stable node» and «stable focus» are missing, but there are equilibrium states such as «unstable node», «unstable focus» and «saddle». The example of detection of the «field of attraction» of the phase trajectory in phase plane is given. Types of «fields of attraction» were identified and economic interpretation for the «fields of attraction» was given. The main directions for the enhancement of the developed software application functionality are formulated. The materials of the article present the practical value for the experts, who are forecasting state of the organization in economy, and particularly in the housing and communal services.
Keywords: : organization, management, housing and utilities, software application, automation, forecasting, qualitative research, dynamic system, phase trajectory, phase point.
NON-STATIONARY TIME SERIES FORECASTING BASED ON
MULTIWAVELET POLYMORPHIC NETWORK
S.N. Verzunov, N.M Lychenko
There are many methods and models for forecasting non-stationary time series. How-ever, the problem of the accuracy and adequacy of the forecast of non-stationary time series has not been solved yet. In this paper, a new forecast model, based on a multiwavelet network with additional customizable parameters, which is called polymorphic, is proposed. The effi-ciency of the proposed model is compared with the well-known time series forecast models like autoregressive integrated moving average model, multilayer perceptron and hybrid model in which both models are combined. Three well-known real data sets (the Wolf’s sunspot data, the Canadian lynx data and the British pound/US dollar exchange rate data) were taken as empirical data. The comparison showed that forecast model based on the proposed multi-wavelet polymorphic network has a smaller prediction error for each series. This is achieved by introducing additional customizable parameters into the wavelet network, which allow to better adapt to the non-stationary nature of time series. Moreover, for the wavelet network to perform well in the presence of linearity, were used linear connections between the wavelet neurons of input and output layers. The proposed technology can be used to predict the time series gen-erated by dynamic processes of a different nature.
Keywords: :forecasting, non-stationary time series, multiwavelet network, additional customizable parameters, ARIMA-model, artificial neural networks, hybrid model.
FUZZY MATHEMATICAL MODELS FOR PREDICTION AND EARLY DIAGNOSIS OF OCCUPATIONAL DISEASES OF AGRICULTURAL WORKERS IN CONTACT WITH PESTICIDES
N.A. Korenevsky, R.V. Stepanov, R.A. Krupchatnikov,
V.V. Aksenov,N.L. Korzhuk
The work is devoted to solving the urgent problem of improving the quality of medical care for workers of agriculture in contact with agricultural chemicals. In the course of the research it was shown that the problem of forecasting and early diagnosis of occupational diseases of agricultural workers employed in crop production belongs to the class of poorly formalized problems with fuzzy data structure, which served as the basis for the choice as the basic apparatus of research methodology of synthesis of hybrid fuzzy decision rules. During the synthesis of fuzzy decision rules, it was found that in order to achieve high quality of decision-making, in addition to risk factors associated with pesticides, the level of psycho-emotional stress, fatigue and ergonomically defective agricultural machinery, environmental risk factors, individual characteristics of the body, etc. should be used as informative features. As a concrete example, the variant of application of the proposed method and information-analytical model in the synthesis of models of forecasting and diagnosis of diseases of the nervous system from the effects on the human body of nitrates-containing pesticides is described. In the course of mathematical modeling and expert evaluation it was shown that the confidence in the decisions exceeds the value of 0.85. The practical application of the proposed method and models will improve the quality of medical services to employees of agriculture providing an increase in working age and reduce disability.
Keywords: agro-industrial complex, occupational diseases, forecasting, early diagnosis, fuzzy hybrid models.