Robust Aeroelastic Optimisation of Composite Plate Wings Subject to Ply Orientation Uncertainty

An approach is presented for the robust stacking sequence optimisation of composite plate wings with uncertain ply orientations. An aeroelastic model is constructed using the Rayleigh-Ritz technique coupled with modified strip theory aerodynamics. Gaussian process emulators are used in conjunction with Support Vector Machine classifiers to construct a surrogate for the discontinuous and non-smooth aeroelastic instability speed, across the space of lamination parameters. The surrogate model is used to estimate the probability that instability occurs at a given design speed, which is minimised using a genetic algorithm. For each evaluation of the objective function, existing data points are reused and the surrogate is updated when required using an adaptive Design of Experiments based upon a modified Latin Hypercube. Optimised stacking sequences are compared to deterministic optima for maximum instability speed. Three layup strategies are undertaken; (i) a benchmark in which ply orientations are limited to 0°, ±45° and 90°, (ii) in which values of ±30° and ±60° are also permitted, and (iii) in which orientations are fixed to 5° increments. Improvements in reliability of at least 83% are achieved using the benchmark layup strategy, with at least 95% and 97% improvements for the second and third strategies respectively. A factor of twenty reduction in the required number of model runs is achieved by using the adaptive surrogate, though this only corresponds to a factor of four reduction in computation time due to the additional time required to fit the surrogate.