Multi-fidelity metamodeling in turbine blade airfoils via transfer learning on manifolds

Uncertainty propagation and sensitivity analysis in expensive engineering design problems require meticulous selection of the experimental data and sophisticated analytic methods, in order to leverage the maximum amount of information that is carried within. Although a metamodeling approach typically suffices as a way to provide a cheap-to-evaluate generative model, classical surrogate methods often fail to accurately describe high dimensional outputs. In this work we attempt to tackle the challenging problem of airfoil shape optimization of a last-stage blade in an industrial gas turbine (IGT). Our proposed methodology consists of applying a manifold learning approach to reduce the output dimensionality of an aerodynamic assessment problem where the effect of the shape parameters of the last stage blade on several performance metrics is investigated. The approach makes use of diffusion maps that identify a low-dimensional embedding on which both low- and high-fidelity data, generated by CFD simulations, reside. Provided that the amount of low-fidelity data typically exceeds the number of high-fidelity experiments, we first construct a metamodel to map the airfoil shape parameters to the reduced low-fidelity outputs. Next, by assuming the existence of domain-invariant features between the output spaces on the two levels of fidelity, we perform transfer learning in order to improve the predictive performance of the initial metamodel so that it honors the available high fidelity data.