Article 1122

Title of the article

Statement and solution of the identification problem of regression analysis method 

Authors

Petr P. Makarychev, Doctor of engineering sciences, professor, head of the sub-department of mathematical support and application of computers, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: pm@pnzgu.ru
Sergey V. Shibanov, Candidate of engineering sciences, associate professor, associate professor of the sub-department of mathematical support and application of computers, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: pm@pnzgu.ru
Aleksandr Yu. Afonin, Candidate of engineering sciences, associate professor of the sub-department of mathematical support and application of computers, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: pm@pnzgu.ru 

Abstract

Background. The object of the research is discrete and continuous models of nonlinear dynamic objects. The subject of the research is the method of constructing models using direct and inverse Laplace transforms, decomposition of the model into linear and nonlinear components, decomposition of the linear part of the model into input and output components. The purpose of this research is to develop a method that provides the construction of both discrete and continuous models of dynamic nonlinear objects for solving problems of structural and parametric identification of parameters by the method of regression analysis of time series based on the results of recording the values of input and output signals with a given time interval. Materials and methods. Developing a method for identifying structures and parameters of dynamic objects’ models, the main provisions of the theory of systems, direct and inverse Laplace transforms, the theory of constructing discrete models, regression and system analysis of time series were used. Results. A method for identifying structures, parameters of discrete and continuous models of objects using regression analysis has been developed. When identifying models, the method provides a search for the number and values of poles, zeros of the transfer function, non-linearity coefficients of the object according to the criterion of the minimum standard deviation of the calculated values from the recorded values of the output signal. Conclusions. The method provides identification of the structure and parameters of discrete and continuous models by the criterion of the minimum standard deviation of the recorded and calculated values of the output signal. The application of the method of constructing and transforming models is possible in combination with various methods of integrating time series. 

Key words

nonlinear dynamic object, parametric identification, least squares regression analysis, discrete and continuous object models 

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For citation:

Makarychev P.P., Shibanov S.V., Afonin A.Yu. Statement and solution of the identification problem of regression analysis method. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University proceedings. Volga region. Engineering sciences. 2022;(1):3–19. (In Russ.). doi:10.21685/2072-3059-2022-1-1

 

Дата создания: 22.04.2022 12:57
Дата обновления: 22.04.2022 13:13