Variable-Fidelity Surrogate Modeling of Lambda Wing Transonic Aerodynamic Performance

Abstract

A new approach to variable-fidelity, gradient-enhanced surrogate modeling using polynomial chaos expansions is presented. An advantage of the new approach is the simultaneous determination of least squares-optimal coefficients for additive and multiplicative low-fidelity corrections as well as the model of interest. This implies that the correction type need not be chosen a priori . The new approach is compared to variable-fidelity, gradient-enhanced kriging also using a hybrid additive-multiplicative bridge. Both methods are tested using two analytic test functions as well as the generation of an aerodynamic database of a vehicle in the transonic and supersonic regimes employing Cart3D and a linearized panel method. Surrogate training points are dynamically selected to reduce model error. Kriging produces greater reductions in root-mean-square-error (RMSE) than polynomial chaos in general, except when the underlying function is an exact polynomial. Both multifidelity approaches achieve reductions in RMSE similar to their monofidelity counterparts at reduced computational expense. The polynomial chaos method benefits more from a multifidelity approach than kriging in terms of error reduction versus computational cost. Forming variable-fidelity surrogates using function values alone tends to perform better than when using gradients in the low-dimensional cases considered here. On the whole, variable-fidelity kriging outperforms varible-fidelity polynomial chaos and monofidelity kriging, and has more favorable properties of training point selection and interpolatory/extrapolatory behavior near the domain boundaries compared to polynomial chaos.