ADAPTIVE SPARSE POLYNOMIAL CHAOS-BASED FLOW FIELD/SONIC BOOM UNCERTAINTY QUANTIFICATION UNDER MULTI-PARAMETER UNCERTAINTIES

The flow field/sonic boom multidisciplinary uncertainty quantification (UQ) and robust design optimization (RDO) techniques for aircraft considering multi-parameter uncertainties have become one of the most promising ways to meet the design requirements of the environment-friendly supersonic civil aircraft. However, traditional aerodynamic UQ methods are expensive, narrow in scope, and encounter the serious curse of dimensionality issue, making it difficult to meet the requirements for complex flow field/sonic boom UQ under multi-parameter uncertainties. To solve this issue, this paper improves the previous adaptive forward-backward selection (AFBS) method, proposes a novel and efficient fully adaptive forward-backward selection (FAFBS) method for sparse polynomial chaos (PC) reconstruction. Compared to the classical forward selection algorithm—the least angle regression (LAR) and orthogonal matching pursuit (OMP), as well as the full PC method, this method fully takes the advantages of the forward selection and backward elimination algorithms, fully adaptively selects the optimal PC bases for the approximation problem and eliminates the redundant ones, thereby avoiding the fitting noise as well as significantly enhancing the sparsity of the candidate PC bases and the reliability of PC reconstruction process. In this paper, two typical complex problems have been used to comprehensively verify the effectiveness and stability of this method, including the classical sonic boom UQ considering temperature, humidity, flight altitude, and Mach number uncertainties, as well as the transonic airfoil aerodynamic UQ considering geometrical and operational uncertainties. The results show that the FAFBS-based PC method achieves the fastest error convergence rate and the smallest approximation error when given the same number of training samples. The convergence rate of the LAR (or OMP)-based PC method is significantly slower than that of the FAFBS-based PC method, while the original full PC method obtains the slowest convergence. Further, for the same accuracy of moment estimation, the computational cost of UQ by using the FAFBS-based PC method is reduced by three orders of magnitude compared to that of UQ by Monte Carlo simulation (MCS) methods, that best meet the requirements for complex flow field/sonic boom UQ and multidisciplinary RDO under multi-parameter uncertainties.