An adjoint-assisted multilevel multifidelity method for uncertainty quantification and its application to turbomachinery manufacturing variability

In this work we propose, analyze, and demonstrate an adjoint-based multilevel multifidelity Monte Carlo (MLMF) framework called FastUQ. The framework is based on the MLMF of Geraci et al. and uses the Inexpensive Monte Carlo (IMC) method of Ghate as low-fidelity surrogate. The setup cost of IMC-1 surrogate in FastUQ requires just the adjoint solution at the input mean whose computational cost is independent of the number of input uncertainties making it suitable for solving problems with a large number of uncertain parameters. We demonstrate the robustness of the method to quantify uncertainties in aerodynamic parameters due to surface variations caused by the manufacturing processes for a highly loaded turbine cascade. A stochastic model for surface variations on the cascade is proposed and optimal dimensionality reduction of model parameters is realised using goal-based principal component analysis using adjoint sensitivities of multiple quantities of interest. The proposed method achieves a 70% reduction in computational cost in predicting the mean quantities such as total-pressure loss and mass flow rate compared to the state-of-art MLMC method.