Mathematical model identification of gas turbine engine with account for initial data uncertainty

DOI: 10.34759/vst-2021-3-171-185

Аuthors

Baturin O. V.^*, Nikolalde P. ..^**, Popov G. M.^***, Korneeva A. I.^****, Kudryashov I. A.^*****

Samara National Research University named after Academician S.P. Korolev, 34, Moskovskoye shosse, Samara, 443086, Russia

*e-mail: oleg.v.baturin@gmail.com
**e-mail: nikopaul_15@hotmail.com
***e-mail: popov@ssau.ru
****e-mail: akorneeva94@mail.ru
*****e-mail: ivan.kudryash1337@gmail.com

Abstract

The computational models used today require unambiguous (deterministic) values of the initial data in order to obtain a solution. In reality, however, the researcher often does not know the exact value of a given quantity. He knows the results of their direct or indirect measurement, which has a margin of error. Awareness of the fact of the initial data uncertainty may lead to a complete rethinking of the computational study process and the interpretation of its results.

In the conducted study, the authors created a stochastic thermodynamic model of the AI-25 gas turbine engine that accounts for the initial data uncertainty.

As the result of the available set of experimental results generalization the most probable values of the measured engine parameters have been found. Based on these, a deterministic thermodynamic model of the AI-25 engine operating process for the selected operating mode was created. Further, an algorithm was developed and implemented, which transformed a deterministic mathematical model of the AI-25 engine operating process at the operating mode of interest into a stochastic one. It allows determining the scatter of outlet parameter values, knowing the scatter of several inlet parameters. The stochastic model has been built on the assumption that the scatter of uncertain inlet data complied with a normal distribution law. Notwithstanding that the thermodynamic model is relatively simple and fast, it requires a huge number of calls to the initial deterministic computational model, which does not allow obtaining stochastic results for all variables of interest in a reasonable time frame.

For this reason, a stochastic solution was being searched for in two stages. At the first stage, a sensitivity analysis was being performed. As the result, the initial data was ranked according to the degree of the end result affecting. A study, in which computation of specific fuel consumption scattering for 2, 3, 4, 5 and 6 first variables of the series was being performed sequentially, was conducted for the sequence obtaining. The scatter of specific fuel consumption values and other important parameters at the selected engine operation mode was changing insignificantly after accounting for more than five affecting variables. The obtained data was transformed into the bell-shaped bivariant distribution on the graph of the parameter of interest dependence on the air consumption. The obtained data herewith was compared with the similar bell-shaped graph, obtained by the experimental data.

With the conventional deterministic approach, computational and experimental results obtained for the same mode are the points of the graph. Their mismatch is being computed in the form of the two differences (deviations) along the two coordinate axes. Given that the errors of the two points being compared determining are not accounted for herewith, the obtained mismatch has an error, which value is unknown. The stochastic approach allows giving a quantitative description of the mismatch. It represents a bell-shaped bivariant distribution, described by the two parameters: the expectation of the difference and the mean-square deviation for the two coordinate axes.

Keywords:

computations uncertainty, initial data uncertainty, computation error, validation, thermodynamic calculation, experiment error, sensitivity analysis, gas-turbine engine

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