Parameterization of a power regression model for aircraft wing mass using a two-criteria estimation method

Аuthors

Bazilevskiy M. P.

Irkutsk State Transport University (IrGUPS), 15, Chernyshevsky str., Irkutsk, 664074, Russia

e-mail: mik2178@yandex.ru

Abstract

The problem of predicting the mass of aircraft at the initial stage of their design, as well as the mass of their individual components, is a significant challenge today. There are various methods for addressing this issue, one of which is to utilize well-established «weight formulas» or to derive new relationships through regression analysis. One of the most significant structural components of large transport aircraft is the wings, and to estimate the mass of these wings various techniques have been developed including those proposed by Thorenbeck, Shevell, Howe, Kundu, Sheinin and Badyagin. Often a power function such as the Cobb-Douglas model is used to describe the relationship between wing mass and influencing factors, and it is necessary to construct a power regression model by taking the logarithm of the equation and estimating the coefficients of the resulting linear model using ordinary least squares. In this paper, we propose a previously developed two-criteria assessment method for parameterizing linear regression models. This method forms a set of Pareto-optimal alternatives, including estimates from the least squares and absolute deviation methods and other similar methods. To create the Pareto set, we solve a series of linear programming problems. We describe a specific algorithm for parameterizing power regression using this two-criterion method. Using the proposed algorithm, it was possible to improve the quality of the previously developed model of aircraft wing mass based on information about thirty-two different aircraft characteristics. In terms of mean absolute error, the improvement was approximately 31%, and in terms of root mean square error, it was 26.4%.

Keywords:

regression analysis, aircraft wing mass, power regression, two-criteria estimation method, ordinary least squares method, least absolute deviations method, linear programming

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