  In the present work, we consider multi-fidelity surrogate modelling to fuse
the output of multiple aero-servo-elastic computer simulators of varying
complexity. In many instances, predictions from multiple simulators for the
same quantity of interest on a wind turbine are available. In this type of
situation, there is strong evidence that fusing the output from multiple
aero-servo-elastic simulators yields better predictive ability and lower model
uncertainty than using any single simulator. Hierarchical Kriging is a
multi-fidelity surrogate modelling method in which the Kriging surrogate model
of the cheap (low-fidelity) simulator is used as a trend of the Kriging
surrogate model of the higher fidelity simulator. We propose a parametric
approach to Hierarchical Kriging where the best surrogate models are selected
based on evaluating all possible combinations of the available Kriging
parameters candidates. The parametric Hierarchical Kriging approach is
illustrated by fusing the extreme flapwise bending moment at the blade root of
a large multi-megawatt wind turbine as a function of wind velocity, turbulence
and wind shear exponent in the presence of model uncertainty and
heterogeneously noisy output. The extreme responses are obtained by two widely
accepted wind turbine specific aero-servo-elastic computer simulators, FAST and
Bladed. With limited high-fidelity simulations, Hierarchical Kriging produces
more accurate predictions of validation data compared to conventional Kriging.
In addition, contrary to conventional Kriging, Hierarchical Kriging is shown to
be a robust surrogate modelling technique because it is less sensitive to the
choice of the Kriging parameters and the choice of the estimation error.
