# Article 2120

 Title of the article IDENTIFICATION OF OBJECT MODEL PARAMETERS BY THE METHOD OF REGRESSION ANALYSIS Authors Bezjaev Viktor Stepanovich, Candidate of engineering sciences, associate professor, sub-department of software and computer applications, Penza State University (40, Krasnaya street, Penza, Russia), E-mail: pm@pnzgu.ru Makarychev Pjotr Petrovich, Doctor of engineering sciences, professor, head of the sub-department of software and computer applications, Penza State University (40, Krasnaya street, Penza, Russia), E-mail: mpp@pnzgu.ru Index UDK 681.5.015.4 DOI 10.21685/2072-3059-2020-1-2 Abstract Background. The procedure of identification of parameters of models of dynamic objects by the method of regression analysis is considered. The substantiation and choice of structure, types of components of the best discrete model, in the form of difference equations of the order are given. The sequence of estimation of numerical values of parameters of discrete model of object, correspondence of these parameters to experimental data is discussed. We propose an integral quadratic criterion for assessing the adequacy of the model using measurements at discrete times. The basic approach of parametric identification is used-the least squares method, which, while respecting linearity and discreteness, provides a simple and universal solution. The questions of estimation of parameters of continuous models on the basis of values of parameters of discrete model are considered Results. The procedure of estimation of parameters of discrete and continuous models of dynamic object on the basis of results of observation of input and output variable on the set interval of time is developed. Conclusions. The structure of the regression model must be consistent with the structure of the continuous and discrete models based on the expected composition of the poles and zeros. The number of zeros and zeros is determined from the condition of the minimum standard deviation of the calculated values from the observed values of the output variable. The optimal value of the poles and zeros is determined by a complete search of possible options. Key words regression analysis, mathematical model of dynamic object, identification of model parameters, continuous model, discrete model Download PDF References 1. Montgomery D. C., Peck E. A., Vining G. G. Introduction to Linear Regression Analysis, 5th Edition. John Wiley & Sons, Inc, 2012, 672 p. 2. Giri I., Chetty P. Procedure and interpretation of linear regression analysis using STATA. 2017. Available at: www.projectguru.in 3. Isermann R., Műnchhof M. Identification of Dynamic Systems. An Introduction with Applications. Berlin: Springer, 2010, 710 p. 4. Mangan N. M., Kutz J. N., Brunton S. L., Proctor J. L. Proceedings of the royal society a. Mathematical, physical and engineering sciences. 2017, vol. 473 (2204). 5. Makarychev P. P. Analiticheskie i chislennye metody modelirovaniya estestvennonauchnykh i sotsial'nykh problem: materialy XII Mezhdunar. nauch.-tekhn. konf. [Analytical and numerical methods for modeling natural-scientific and social issues: proceedings of XII International scientific and practical conference]. Penza, 2017, pp. 113–117. [In Russian] 6. Diligenskaya A. N. Identifikatsiya ob"ektov upravleniya [Identification of management objects]. Samara: Samar. gos. tekhn. un-t, 2009, 136 p. [In Russian] 7. Volgina M. A., Makarychev P. P. Modelirovanie mnogokomponentnykh sistem na osnove markirovannykh grafov: monografiya [Simulation of multicomponent systems based on marked graphs: monograph]. Penza: Izd-vo PGU, 2011, 156 p. [In Russian] 8. Makarychev P. P. Modelirovanie nepreryvnykh i diskretnykh dinamicheskikh sistem: ucheb. posobie [Modeling of continuous and discrete dynamical systems: teaching aid]. Penza: Izd-vo Penz. politekh. in-ta, 1988, 76 p. [In Russian] 9. Makarychev P. P., Afonin A. Yu., Shibanov S. V. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki [University proceedings. Volga region. Engineering sciences]. 2019, no. 2 (50), pp. 11–22. [In Russian] 10. Dreyper N., Smit G. Applied Regression Analysis. 3d ed. Moscow: Dialektika, 2007, pp. 912. 11. Semenychev V. K., Semenychev E. V. Parametricheskaya identifikatsiya ryadov dinamiki: struktury, modeli, evolyutsiya: monografiya [Parametric identification of the dynamics’ series: structures, models, evolution: monograph]. Samara: Izd-vo SpmNTs RAN, 2011, 364 p. [In Russian]

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