Multi-fidelity nonlinear unsteady aerodynamic modeling and uncertainty estimation based on Hierarchical Kriging

Abstract

By fusing aerodynamic data from multiple sources, multi-fidelity methods can well balance model accuracy and computational cost. To extend multi-fidelity models for predicting unsteady aerodynamics with uncertainty estimation, an improved modelling framework based on the Hierarchical Kriging (HK) is proposed for nonlinear aerodynamic reduced-order modelling. This aerodynamic modelling framework is achieved by a two-stage modelling strategy. In the first stage, using the current and time-delayed low-fidelity aerodynamic load and pitching motion as input, a linear regression model is built to achieve preliminary aerodynamic prediction. In the second stage, the current and time-delayed preliminary prediction, as well as pitching motion history are used as the input of the Hierarchical Kriging model to predict the high-fidelity aerodynamic loads. The generalization capability of this improved modelling framework is firstly verified by several analytical examples. Furthermore, with three sets of training samples taken from harmonic pitching motions of an airfoil in transonic flow, the proposed model achieves accurate prediction on unsteady aerodynamics of other harmonic and random motions, and provides reliable uncertainty estimation of the predicted unsteady aerodynamics. In addition, the computational cost and prediction errors of multi-fidelity and the single-fidelity aerodynamic model are compared. Even with the same computational cost, the proposed multi-fidelity model still shows improved accuracy. Finally, using the uncertainty estimation of the proposed model, an active learning task is performed, which actively selects and incrementally adds the required training samples. With active learning, a good balance between model accuracy and cost of data acquisition is maintained, while avoiding over-fitting problems of the proposed model.