Multi-disciplinary optimization of aircraft wing design with using proper orthogonal decomposition and inductive design exploration method under uncertainty

The robust optimization of aircraft wings with uncertainties has a large number of design variables due to the complex parametric geometry definitions. The increase in the number of variables in robust optimization problems causes high computational cost. Therefore, reducing the number of design variables and the design complexity is of great importance for robust optimization. As a solution to these problems, the computational load is reduced by integrating the proper orthogonal decomposition method with the inductive design exploration method. The proper orthogonal decomposition method is a dimensional reduction method and analyses the wing design variables in the robust optimization process and extracts the dominant features. Using the calculated dominant features, the wing geometry is re-parametrized by using fewer design variables and an advantage is obtained in terms of computational cost. Thanks to the inductive design exploration method, the uncertainties in both the design inputs and the simulation models were incorporated into the calculations by considering the design requirements and constraints, and robust designs were calculated. The underlying idea of the inductive design research method is to determine the level of robustness of design alternatives, called the robustness criterion. The robust designs calculated for this purpose were compared in terms of performance function and robustness criteria, and their advantages and disadvantages were evaluated. Another problem in the robust optimization process is that the use of high-precision computational fluid dynamics and finite element analyses increases the computational time, especially in multidisciplinary studies where both aerodynamic and structural requirements are considered. Therefore, the computational burden resulting from the use of high accuracy computational methods has been reduced with the proper orthogonal decomposition based radial function surrogate model and the design space has been investigated. The ability of the surrogate model used to predict the design results was also compared with the values calculated from computational fluid dynamics and finite element analysis, and the efficiency of the method used was evaluated. There are differences between the calculated and manufactured designs due to the uncertainties that occur during design. Therefore, determining the uncertainties for a robust multidisciplinary optimization study is another important issue. In this study, the uncertainties arising from the turbulence model used in the computational fluid dynamics analysis were determined using the eigenspace perturbation method. In this way, the variation of the design results under the uncertainties caused by the turbulence model is calculated. In the structural optimization process, which includes issues such as the strength of the internal structure of the wing and the weight of the wing, the lattice cell structures were used and the uncertainties arising from the manufacture of the lattice cells were also calculated and included in the robust optimization study.