Uncertainty Quantification for Multi-Dimensional Correlated Flow Field Responses

The inherent randomness of fluid dynamics problems or human cognitive limitations results in non-negligible uncertainties in CFD modeling and simulation, leading to doubts about the credibility of CFD results. Therefore, scientific and rigorous quantification of these uncertainties is crucial for assessing the reliability of CFD predictions and informed engineering decisions. Although mature uncertainty propagation methods have been developed for individual output quantities, the challenges lie in the multi-dimensional correlated flow field variables. This article proposes an advanced uncertainty propagation modeling approach based on proper orthogonal decomposition and artificial neural networks. By projecting the multi-dimensional correlated responses onto an orthogonal basis function space, the dimensionality of output is significantly reduced, simplifying the subsequent model training process. An artificial neural network that maps the uncertain parameters of the CFD model to the coefficients of the basis functions is established. Due to the bidirectional representation of flow field variables and basis function coefficients through proper orthogonal decomposition, combined with artificial neural network modeling, rapid prediction of flow field variables under any model parameters is achieved. To effectively identify the most influential model parameters, we employ a multi-output global sensitivity analysis method based on covariance decomposition. Through two exemplary cases of NACA0012 airfoil and M6 wing, we demonstrate the accuracy and efficacy of our proposed approach in predicting multi-dimensional flow field variables under varying model coefficients. Large-scale random sampling is conducted to quantify the uncertainties and identify the key factors that significantly impact the overall flow field.