Applications of multi-fidelity multi-output Kriging to engineering design optimization

Surrogate modelling is a popular approach for reducing the number of high fidelity simulations required within an engineering design optimization. Multi-fidelity surrogate modelling can further reduce this effort by exploiting low fidelity simulation data. Multi-output surrogate modelling techniques offer a way for categorical variables e.g. the choice of material, to be included within such models. While multi-fidelity multi-output surrogate modelling strategies have been proposed, to date only their predictive performance rather than optimization performance has been assessed. This paper considers three different multi-fidelity multi-output Kriging based surrogate modelling approaches and compares them to ordinary Kriging and multi-fidelity Kriging. The first approach modifies multi-fidelity Kriging to include multiple outputs whereas the second and third approaches model the different levels of simulation fidelity as different outputs within a multi-output Kriging model. Each of these techniques is assessed using three engineering design problems including the optimization of a gas turbine combustor in the presence of a topological variation, the optimization of a vibrating truss where the material can vary and finally, the parallel optimization of a family of airfoils.