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Документ Assessing and forecasting the state of deteriorating systems with the use of modified regression polynomials on the basis of functional approximation of their coefficients(Національний технічний університет "Харківський політехнічний інститут", 2023) Raskin, Lev; Sukhomlyn, Larysa; Sokolov, Dmytro; Vlasenko, VitaliiObject of research is technical state of deteriorating systems whose operating conditions depend on a large number of interacting factors. The caused inhomogeneity of the sample of initial data on the technical state leads to impossibility of correct use of traditional methods of assessing the state of a system (meaning methods using mathematical tools of regression analysis). Subject of research is developing a method for constructing a regression polynomial based on the results of processing a set of controlled system parameters. Non-linearity of the polynomial describing the evolution of the technical state of real systems leads to an increase in the number of regression polynomial coefficients subject to estimation. The problem is further complicated by the growing number of factors affecting the technical state of the system. In these circumstances, the so-called occurs. Goal the research consists in developing a method for constructing an approximation polynomial that describes evolution of the system state in a situation where the volume of the initial data sample is insufficient for correct estimating coefficients of this polynomial. The results obtained. The paper proposes a method for solving the given problem, based on implementation of a two-stage procedure. At the first stage a functional description of the approximation polynomial coefficients is performed; and this radically reduces the number of regression polynomial parameters to be estimated. This polynomial is used for preliminary estimation of its coefficients with the aim of filtering out insignificant factors and their interactions. At the second stage, parameters of the truncated polynomial are estimated by means of using standard technologies of mathematical statistics. Two approaches to constructing a modified polynomial have been studied: the additive one and the multiplicative one. It has been shown that the additive approach is, on average, an order of magnitude more effective than the multiplicative one.Документ Evaluation of system controlled parameters informational importance, taking into account the source data inaccuracy(Національний технічний університет "Харківський політехнічний інститут", 2023) Raskin, Lev; Sukhomlyn, Larysa; Sokolov, Dmytro; Vlasenko, VitaliiThe purpose of the study is to improve the standard methodology for controlled parameters information value assessing. The proposed method is based on the controlled parameters value probabilities analysis falling into the subintervals of the interval of possible values for different states of the system. When the value of the controlled parameter falls into the left or right boundary subintervals of the compatibility interval for any state of the object, the conclusion about its state is made taking into account possible errors of the first or second kind in this case. When the controlled parameter value enters the central subinterval, useful information appears if the corresponding probabilities for the states H₁ and H₂ are differ significantly. Thus, it is shown that taking into account the probabilities of fuzzy values of the controlled parameter falling into the compatibility interval for various states of the object significantly increases its informational value.Документ Mitigation of negative impact of cement plant on the adjacent grounds(ТОВ "Планета-Прінт", 2021) Krivileva, S.; Vlasenko, VitaliiДокумент Multi-criteria evaluation of the multifactor stochastic systems effectiveness(Національний технічний університет "Харківський політехнічний інститут", 2023) Raskin, Lev; Sukhomlyn, Larysa; Sokolov, Dmytro; Vlasenko, VitaliiSubject of the research in the article is the evaluation of complex multifactor stochastic systems functioning effectiveness according to a variety of correlated criteria. The problem actuality is determined by the fact that an independent evaluation of system effectiveness for each of the mutually correlated criteria for the system under consideration is not informative. In well-known works in the direction of multiple correlation, a relatively simple problem of estimating the correlation between one resulting parameter and a set of influencing factors is considered, which is not enough for the analysis and management of multicriteria systems. In addition, the known results do not take into account possible significant differences in influencing factors mutual cor relation values. Purpose of Work is to develop a methodology for a comprehensive assessment of system effectiveness according to a variety of interrelated criteria. Tasks to be Solved: splitting the set of system parameters into two subsets (parameters determining the effectiveness of system and parameters affecting it), forming additive convolutions of parameters included in subsets, developing a methodology for calculating the multiple correlation coefficient between the components of the selected subsets, developing a method for differentiating a scalar function from a vector argument by this argument. Applied Methods: nonlinear programming, multidimensional correlation analysis, method of differentiation of scalar functions by vector argument. These methods are used for forming and calculating a multiple correlation coefficient between the set of system effectiveness complex criterion components values and its control parameters set values. Results Obtained: proposed methodology provides the possibility of solving the problems of system management, taking into account the revealed relationship between the multi-criteria evaluation of system effectiveness and values of its controlled parameters. At the same time, an important advantage of the obtained result lies in the possibility that arises when using it to take into account the joint (group) influence of control variables on the complex criterion of system efficiency. The developed technology of scalar functions differentiation by vector argument has great practical importance which expands the arsenal of computational mathematics.