Reliability based optimization in aeroelastic stability problems using polynomial chaos based metamodels

In this work, reliability based design optimization (RBDO) of two aeroelastic stability problems is addressed: (i) divergence, which arises in static aeroelasticity, and (ii) flutter, which arises in dynamic aeroelasticity. A set of design variables is considered as random variables, and the mean mass is minimized for a given set of constraints — including the probability of failure by divergence or flutter. The optimization process requires repeated evaluation of reliability, which is a major contributor to the total computational cost. To reduce this cost, a polynomial chaos expansion (PCE)-based metamodel is created over a grid in the parameter space. These precomputed PCEs are then interpolated for reliability calculation at intermediate points in the parameter space, as demanded by the optimization algorithm. Two new modifications are made to this method in this work. First, the Gauss quadrature rule is used — instead of statistical simulation — to estimate the chaos coefficients for higher computational speed. Second, to increase this computational gain further, a non-uniform grid is chosen instead of a uniform one, based on relative importance of the design parameters. This relative importance is found from a global sensitivity analysis. This new modified method is applied on a rectangular unswept cantilever wing model. For both optimization problems, it is observed that the proposed method yields accurate results with a considerable computational cost reduction, when compared to simulation based methods. The effect of grid spacing is also explored to achieve the best computational efficiency.