Aleksandr M. Kler, Vitalii E. Alekseiuk, Anatolii A. Levin, Polina V. Khan

1Melentiev Energy Systems Institute SB RAS, Irkutsk National Research Technical University

The purpose of this study is to develop an effective method for processing the results of thermophysical experiments based on solving two types of nonlinear mathematical programming problems. The article provides a description of the proposed method for identifying the coefficients of the mathematical model of a thermophysical experiment based on the results of measured experimental data. We also consider two mathematical models that interpret the results of the performed field experiments. The technique presented in the article is based on the maximum likelihood method and takes into account the relative errors of all sensors used to obtain the values of the measured parameters. Moreover, the technique involves a two-stage approach in solving the problem of identifying the  parameters of a mathematical model. At the first stage, the maximum relative error among the measured parameters is minimized, which makes it possible to identify and eliminate "bad" measurements. Further, at the second stage, the sum of the modules of relative errors of all measured parameters is minimized. Computational experiments have shown that this approach is more efficient than the  classical least squares method, which is sensitive to the presence of "bad" measurements and, under certain conditions, can become a ravine function. The last section of the article presents the results of computational experiments testing the proposed method. Calculations have shown that this approach is very effective and allows you to adjust the coefficients of mathematical models with high accuracy.

thermophysical experiment, identification of parameters, nonlinear mathematical programming, relative error, measured parameters, maximum likelihood criterion, method of least modules, mathematical model