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.

中文翻译：

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不确定度量化的辅助多级多保真度方法及其在涡轮机械制造变异性中的应用

在这项工作中，我们提出，分析和演示了一个称为FastUQ的基于伴随的多级多保真蒙特卡洛（MLMF）框架。该框架基于Geraci等人的MLMF。并使用Ghate的廉价Monte Carlo（IMC）方法作为低保真替代品。FastUQ中IMC-1代理的设置成本仅需要输入均值的伴随解，其计算成本与输入不确定性的数量无关，因此适合解决具有大量不确定参数的问题。我们证明了该方法的可靠性，该方法可以量化由于高负荷涡轮机叶栅的制造工艺引起的表面变化而导致的空气动力学参数不确定性。提出了一种用于级联表面变化的随机模型，并使用基于目标的主成分分析并使用多个感兴趣量的伴随敏感度，实现了模型参数的最佳降维。与最新的MLMC方法相比，该方法在预测平均量（例如总压力损失和质量流率）方面，可将计算成本降低70％。