Multi-fidelity surrogates from shared principal components

Abstract

Computational cost of high-fidelity simulations limits the number of evaluations which may be performed in design exploration and optimization. Surrogates based on samples of multiple fidelities are used to decrease computational cost and lower error from single-fidelity surrogates. This paper develops a novel multi-fidelity surrogate model based on principal components which are shared between multiple fidelities of finite element model samples. This method does not require a common grid between the fidelities, further reducing computational cost. The new method was tested on various design spaces of the Transonic Purdue Research Compressor and compared to other common and novel multi-fidelity methods. The new method was more accurate and required less computational cost than the other tested methods. Little to no increase in computational cost was needed to reduce surrogate error to 50% of the single-fidelity error. For fixed error, the computational cost was reduced by more than 75%. These results were also validated by testing the method on a more complex turbomachinery blade, Parametric Blade Study Rotor 4. The decreased error and computational cost improve effectiveness of design exploration and optimization. Such improvements help meet the demand for cleaner and safer engines by allowing high-fidelity design exploration within reasonable time frames.