01. Kantor О.G., Spivak S.I., Morozkin N.D. Parametric Identification of the Models with Specified Quality Characteristics

UDK 519.6

DOI: 10.15507/2658-4123.029.201904.480-495

Parametric Identification of the Models with Specified Quality Characteristics

Olga G. Kantor
Associate Professor of the Chair of Corporate Finance and Accounting Technologies, Ufa State Petroleum Technological University (1 Kosmonavtov St., Ufa 450062, Russia), Ph.D. (Physics and Mathematics), ResearcherID: O-5136-2015, ORCID: https://orcid.org/0000-0002-3186-3285, ScopusID: 26767794600, This email address is being protected from spambots. You need JavaScript enabled to view it.

Semen I. Spivak
Head of Chair of Mathematical Modeling, Bashkir State University (32 Zaki Validi St., Ufa 450076, Russia), D.Sc. (Physics and Mathematics), Professor, ResearcherID: B-9334-2017, ORCID: https://orcid.org/0000-0002-0911-7446, ScopusID: 16465463600, This email address is being protected from spambots. You need JavaScript enabled to view it.

Nikolay D. Morozkin
Rector of Bashkir State University (32 Zaki Validi St., Ufa 450076, Russia), D.Sc. (Physics and Mathematics), Professor, ResearcherID: D-2570-2019, ScopusID:6603118906, This email address is being protected from spambots. You need JavaScript enabled to view it.

Introduction. The model of a given structure should be identified based on the results of solving the problem of parametric identification. This model should provide the best possible the database development reproduction of the experimental data. The concept of “best” is not strictly structured. Therefore, the procedure for identifying such a model is subject to natural logic and includes the stages of data a determination of a set of acceptable models and subsequent selection of the best of them. If the set of acceptable models is large, the procedure for determining the best one can be time-consuming. In this regard, the development of methods for parametric identification, which at the stage of creating a set of acceptable models allows taking into account the qualitative aspects of the identified dependence, which are of interest to the researcher, is of particular importance.
Materials and Methods. The set of acceptable methods in the problems of parametric identification largely depends on the type of the experimental data. Uncertainty for example, probabilistic and statistical methods are useful if the observed factors are random and subject to any law of probability distribution. If the conditions for the use of such methods are not met, it may be useful to present an approach based on identifying the boundaries of location of the model parameters that ensure the achievement of specified levels of quality characteristics.
Results. The procedure of parametric identification of models is formalized. It is based on the use of maximum permissible parameter estimates and allows one to determining the set of parameter values that guarantee the achievement of the required qualitative level of experimental data description, including from the standpoint of analyzing the impact of changes in accord with requirements to the accuracy of their reproduction. The approbation of the developed method on the example of the construction of a one-factor model of chemical kinetics is presented.
Discussion and Conclusion. It is shown that the obtained value of the chemical reaction rate constant, in accordance with the introduced criteria, provides acceptable accuracy, adequacy, and stability of the identified kinetic model. At the same time, the results of calculations revealed the information that can form the basis for planning experiments carried out in order to improve the accuracy of the experimental data.

Keywords: parametric identification, maximum allowable estimates, approach of L.V. Kantorovich, models’ quality

For citation: Kantor О.G., Spivak S.I., Morozkin N.D. Parametric Identification of the Models with Specified Quality Characteristics. Inzhenerernyye tekhnologii i sistemy = Engineering Technologies and Systems. 2019; 29(4):480-495. DOI: https://doi.org/10.15507/2658-4123.029.201904.480-495

Contribution of the authors: O. G. Kantor – formulation of the basic concept, goals and objectives of the study, calculations, preparation of the text, drawing conclusions; S. I. Spivak – scientific guidance, analysis of the research results, revision of the text, correction of the conclusions; N. D. Morozkin – correction of the literary analysis, revision of the text, correction of the conclusions.

All authors have read and approved the final manuscript.

Received 06.05.2019; revised 06.06.2019;
published online 31.12.2019

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