Multi-Fidelity Kriging Extrapolation

Abstract

Surrogate modelling techniques such as Kriging are a popular means for cheaply emulating the response of expensive Computational Fluid Dynamics simulations. These surrogate models are often used for exploring a parameterised design space and identifying optimal designs. Multi-fidelity Kriging extends the methodology to incorporate data of variable accuracy and costs to create a more effective surrogate. This work recognises that the grid convergence property of CFD solvers is currently an unused source of information and presents a novel method that, by leveraging the data structure implied by grid convergence, could further improve the performance of the surrogate model and the corresponding optimisation process. Grid convergence states that the simulation solution converges to the true simulation solution as the grid is refined. The proposed method is tested with several problems involving both synthetic and realistic multi-fidelity data acquired with Computational Fluid Dynamics simulations. The synthetic results indicate that our method surpasses the most well-known multi-fidelity Kriging model in terms of both accuracy and cost given the proper conditions. The performances of both surrogates in the optimisation cases using Computational Fluid Dynamics simulations were similar. Data-supported conditions for the proposed method to be effective, and a procedure to cheaply recognise them, are provided. To further improve and validate the method, recommendations are given at the end.