Fast Adjoint-assisted Multilevel Multi delity Method for Uncertainty Quanti cation of the Aleatoric Kind

Abstract

In this thesis an adjoint-based multilevel multi delity Monte Carlo (MLMF) method is proposed, analysed, and demonstrated using test problems. Firstly, a multifi delity framework using the approximate function evaluation [1] based on the adjoint error correction of Giles et al. [2] is employed as a low fidelity model. This multifi delity framework is analysed using the method proposed by Ng and Wilcox [3]. The computational cost reduction and accuracy is demonstrated using the viscous Burgers' equation subject to uncertain boundary condition. The multi fidelity framework is extended to include multilevel meshes using the MLMF of Geraci [4] called the FastUQ. Some insights on parameters affecting computational cost are shown. The implementation of FastUQ in Dakota toolkit is outlined. As a demonstration, FastUQ is used to quantify uncertainties in aerodynamic parameters due to surface variations caused by manufacturing process. A synthetic model for surface variations due to manufacturing process is proposed based on Gaussian process. The LS89 turbine cascade subject to this synthetic disturbance model at two o -design conditions is used as a test problem. Extraction of independent random modes and truncation using a goal-based principal component analysis is shown. The analysis includes truncation for problems involving multiple QoIs and test conditions. The results from FastUQ are compared to the state-of-art SMLMC method and the approximate function evaluation using adjoint error correction called the inexpensive Monte Carlo method (IMC). About 70% reduction in computational cost compared to SMLMC is achieved without any loss of accuracy. The approximate model based on the IMC has high deviations for non-linear and sensitive QoI, namely the total-pressure loss. FastUQ control variate effectively balances the low fi delity model errors and additional high fidelity evaluations to yield accurate results comparable to the high fidelity model.