ASSESSING AND FORECASTING THE STATE OF DETERIORATING SYSTEMS WITH THE USE OF MODIFIED REGRESSION POLYNOMIALS ON THE BASIS OF FUNCTIONAL APPROXIMATION OF THEIR COEFFICIENTS
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Abstract
Object 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 <small sample effect> 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.
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