Normality Criteria While Processing Experimental Studies of Gas Turbine Engines Parameters Based on Applied Mathematical Statistics' Methods

Аuthors

Vovk M. Y.^1*, Kulalaev V. V.^2**

1. Lyulka Experimental Design Bureau, branch of the United Engine Corporation – Ufa Engine Industrial Association, 13, Kasatkina str., Moscow, 129301, Russia
2. Lyulka Desing Bureau, 13, Kasatkina str., Moscow, 129301, Russia

*e-mail: mihail.vovk@okb.umpo.ru
**e-mail: kulalayev.viktor@gmail.com

Abstract

The article performed the generalized analysis of normality distribution criteria for experimental data processing [1-20]. A new «vector» criterion and design technique were suggested and examples of distribution normality verification were given, allowing employ the limited volume of experimental data, which was a rather significant factor while gas turbine engines (GTE) tests performing. The new technique of the distribution normality evaluation while analyzing the field of the GTE workbench tests was imposed by the fact that the vast majority of the experimental data used in engineering are subjected to the normal distribution law [1-5, 8-10]. In the applied mathematical statistics in practical regard the probability distribution characteristics are considered as a center of the statistical data grouping, the degree of dissipation and random values behavior in the vicinity of the center. The symmetry relative to the distribution center is also being analyzed. In terms of applied mathematics, analysis of distributed statistics herewith requires certain knowledge, practice and intuition while primary analysis of the set of the experimental data, where subjective factor gains a significant role. The state-of-the-art condition of the GTE tests development based on applied mathematical statistics requires introduction of reliable and powerful evaluation criteria of statistical data, which possess the property of algorithmization. It reduces to minimum the subjective approaches and determines the topicality of the scientific problem, considered in the article.

While identification of a mathematical model in global software accordint

While identifying a gas turbine engine mathematical model in the global software complexes by the experimental data of a definite engine series and performing also the regressive analysis the accomplishment of condition of the normal field distribution of the experimental data is required. Thus, to ensure the validity of the regression analysis the mandatory preliminary analytical verification of the normal distribution law with the normality criteria [8-10, 13-20] in place is required. Currently, there are 21 fitting criteria, modified for the normality distribution verification [8]. The types of the fitting criteria with the normal distribution law (normality criteria) are widely presented in the bulk work [8]. The table of the strength of various criteria of the normal distribution is presented ibid [Table № 80, p.278]. The following specifics of the known fitting criteria should be noted: the criteria work well with the sample values from 8 to 5000 and require employing special tables, requiring precalculation (ex. Shapiro-Wilk criteria, Filliben, La Breck and etc.). Practically, the wellknown criteria calculations require compilng voluminous tables for the subjective analysis, which leads to serious labor costs, and requires “...not only knowledge, practice, intuition” [8], but also considerable constraints of computer employing. The newly introduced normality distribution criterion [Kr1] may be used for the experimental points array processing and regressive statistics analysis for the rig testing of various types of gas turbines and possesses algorithmization features for computer calculations. It may be employed also for creating applied the software global complexes for automated experimental data arrays processing with sufficient shortening of time and design scope on the computer including experimental dataprocessing for actual gas turbine engine tests verification.

Keywords:

criterion, model, regressive analysis, normal distribution law, statistics, applied mathematics, sample, algorithm

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