Oliinyk I. Identification of parameters of interval models of static systems based on the methods for optimal design of a saturated experiment

Dissertation is devoted to solving the actual scientific and applied problem of reducing the computational complexity of the methods of parametric identification of interval models of static systems with guaranteed prognostic properties, by creating new methods of ellipsoid estimation of a set of parameters values. It is analyzed and substantiated that in order to solve problems in conditions of bounded error values. It is expedient to use methods of interval analysis of data. Methods of solving the interval system of linear algebraic equations, in particular methods of interval estimation, ellipsoid estimation and allocation of the "saturated" block by interval system of linear algebraic equations are analyzed, and their defects are established. Based on the results of the analysis of the methods of estimating the area of parameters, the using of the method with localization of interval system of linear algebraic equations solutions in the form of a "saturated" block was substantiated. The method for ellipsoid estimation of the set of parameters values of interval models of static systems is developed, in which, unlike the existing ones, iterative computational scheme of optimal design of the experiment was applied which provided decrease of computational complexity in comparison with known methods. The method of optimal saturated design of experiments in the case of interval representation of output variables of static systems models is developed, which, unlike existing ones, is based on the iterative computational procedure of optimization of predictive properties of interval models. The method of parametric identification of interval models of static systems is improved, which is constructed by combining the advanced ISLAE reduction method and the newly developed method of ellipsoid estimation of the set of parameters values of the interval models of static systems. Based on the methods developed in the dissertation research, with the application of the created software system, an intermediate model of the characteristics of a small hydroelectric power station and an interval model of the daily change in the concentration of harmful emissions of nitrogen dioxide, depending on the traffic intensity, relative humidity and air temperature, were constructed.