МЕТОД СТРУКТУРНОЇ ІДЕНТИФІКАЦІЇ НЕЛІНІЙНИХ МОДЕЛЕЙ СТАТИЧНИХ СИСТЕМ НА ОСНОВІ ІНТЕРВАЛЬНИХ ДАНИХ

Volodymyr  Manzhula; Mykola Dyvak; Andrii Melnyk

doi:10.31649/1999-9941-2024-59-1-94-104

Authors

Volodymyr Manzhula West Ukrainian National University, Ternopil
Mykola Dyvak West Ukrainian National University, Ternopil
Andrii Melnyk West Ukrainian National University, Ternopil

DOI:

https://doi.org/10.31649/1999-9941-2024-59-1-94-104

Keywords:

interval data, interval nonlinear model, structural identification, optimization problem, objective function, gradient

Abstract

Abstract. The article considers an important scientific task of further development of methods for identifying interval nonlinear models of static characteristics of complex objects based on the use of procedures that reduce computational complexity. The proposed approach to mathematical modeling of static characteristics of non-linear objects, based on interval data analysis, ensures the construction of adequate models with guaranteed prognostic properties. The process of constructing interval nonlinear models of the static characteristics of complex objects is based on an optimization problem with a nonlinear objective function that ensures the minimization of the mean square deviation between the values of the simulated static characteristics of the complex object and the values belonging to the experimental intervals. This approach leads to the expansion of the parameter space of nonlinear interval models due to the introduction of additional α coefficients into the objective function, but at the same time, it makes it possible to reduce the optimization problem with a system of nonlinear constraints to a problem without constraints. The main result of the conducted research is a new method of synthesis of the model structure based on the analysis of the gradient of the objective function of the optimization problem for a different set of structural elements. The basis of the development of this method is a new procedure for selecting structural elements of models, which makes it possible to reduce the number of iterations of parametric identification at the stage of forming candidate model structures. The article defines and substantiates the necessary and sufficient conditions for the completeness or optimality of a set of structural elements based on the analysis of the gradient of the objective function and formulates the basic rules for forming a set of these elements in the model. Based on theoretical and practical considerations, an algorithm for implementing a new method of structural identification is proposed, and its convergence is demonstrated in the example of modeling of small hydropower facilities. The proposed method of identifying nonlinear models based on the analysis of interval data ensures the development of applied research in the fields of national defense, environmental protection, medicine, and other fields where mathematical models are the basis for decision-making.

Author Biographies

Volodymyr Manzhula, West Ukrainian National University, Ternopil

Cand. of Tech. Sc., Associate Professor, Doctoral Student of the Department of Computer Science

Mykola Dyvak, West Ukrainian National University, Ternopil

Doctor of Technical Sciences, Professor, Vice-Rector for Scientific Work, West Ukrainian National University, Ternopil

Andrii Melnyk, West Ukrainian National University, Ternopil

Doctor of Technical Sciences, Professor, Professor of the Department of Computer Science, West Ukrainian National University, Ternopil

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