Studying Surrogate Model Application in the Problem of the Wing Geometrical Optimization Problem Considering Flutter

Аuthors

Chen L. ^*, Strelets D. Y.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: lechen@mai.education
**e-mail: dimstrelets@rambler.ru

Abstract

Optimization of the wing considering aeroelasticity is a multi-stage problem. In the first stage, an aeroelastic model of the wing, which includes the analysis of deformation and critical flutter velocity of the wing, is being created. The second stage is the task of the design variables optimizing. Optimization problems in aeronautical engineering often involve several design variables, and the relationships between the input and output data are nonlinear. Thus, such problems are being characterized by a long computational time and low optimization efficiency. Surrogate models application in optimization problems in aviation may significantly improve the design efficiency.
This article considers both stages. When creating an aeroelastic model, only the effect of flutter is being considered. The aspect ratio and taper of the wing are used as design variables in the optimization problem. Maximum critical flutter velocity and maximum lift coefficient are being considered as the optimization objectives. Based on the experimental design theory, an optimal sample of the Latin hypercube is used for the data obtaining on the sample points for the Kriging model construction. The flutter simulation was performed with the NASTRAN SOL 145. The shell element and doublet lattice methods were used by the structural and aerodynamic models, respectively, and infinite plate splines were used to complete the aerodynamic-structural interpolation. At the same time, the vortex lattice method is being employed in the aerodynamic computations to determine the total lift and its coefficient. The optimization algorithm is the NSGA-2non-dominated sorting genetic algorithm. The results dempnstrate that the optimization method based on the Kriging model allows for a relatively accurate expression of the relationship between the geometric variables and the critical flutter velocity, as well as obtaining a set of Pareto solutions with a smaller amount of computation, which ensures the solution of more complex optimization problems.

Keywords:

surrogate model, Kriging model, multi-criteria optimization, wing geometrical optimization, non-dominated sorting genetic algorithm II, wing flutter, response surface

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