Combination of Polynomial Chaos with Adjoint Formulations for Optimization Under Uncertainties

The main idea of this approach is to combine the non-intrusive polynomial chaos-based uncertainty quantification methods with adjoint formulations for optimization under uncertainties. Introducing uncertainties in a design process, the objective is also uncertain. Using polynomial chaos expansion, the uncertain objective can be characterized by its mean and its variance. Therefore, it becomes a multi-objective problem and gradient-based optimization requires the gradient of both quantities. These gradients are obtained from the polynomial chaos expansion of the gradient of the objective. The proposed approach is applied to the optimal shape design of the transonic RAE2822 airfoil under uncertainties. The optimization procedure is performed using a Python-based optimizer SciPy which uses the sequential least square programming (SLSQP) algorithm.

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