Surrogate-based robust design optimization by using Chebyshev-transformed orthogonal grid

Surrogate-based aerodynamic robust design optimization uses a surrogate model to calculate the robustness indices, which strongly relies on the overall accuracy of the model, as well as the efficient exploration of the design space. For most surrogate modeling approaches, significant inaccuracies are often observed at the outlier region of the design space, where very few samples are spotted. A novel method using Chebyshev transformation is applied to re-allocate the orthogonal Latin hypercube sample set to alleviate the corner errors and eventually improve the overall accuracy. An inner Kriging model is developed using the sampling method, and robustness indices are calculated based on the subspaces adjacent to the sampling points. Subsequently, an outer robust model is constructed with the robustness indices as the target. Ultimately, a combination of the inner and outer models is utilized with the genetic algorithm to accomplish multi-objective robust optimization. Theoretical tests are undertaken for classic test functions, showing the advantage of the proposed approach. Based on this method, aerodynamic robust design optimizations are carried out on the RAE 2822 airfoil, for which the lift coefficient and drag coefficient are optimized for a given range of geometrical parameters. An increase of 1.94% lift coefficient and a reduction of 2.53% drag coefficient are achieved compared to the baseline design without sacrificing the robust performances.