基于自适应稀疏多项式混沌的流场/声爆多源不确定量化技术研究

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

考虑不确定性的飞行器流场/声爆多学科不确定量化和稳健优化设计技术已经成为满足未来环保型超音速民机设计要求最有希望的途径之一.然而传统的飞行器气动不确定量化方法花费巨大,适用范围窄,并遭遇了严重的维数灾难难题,难以满足复杂流场/声爆多源不确定性量化需求.针对这一难题,文章改进了前期提出的自适应前向−后向选择(AFBS)算法,提出了一种基于全自适应前向−后向选择(FAFBS)的高效稀疏多项式混沌(PC)重构方法.该方法相对于经典的前向选择算法——最小角回归(LAR)和正交匹配追踪(OMP)以及全PC方法,其充分结合了前向选择和后向消除算法的优势,全自适应地选择对近似问题最优的PC项,并剔除掉不重要的PC项,从而避免了拟合噪声的产生,显著加强了PC重构的稀疏性和拟合过程的可靠性.文章使用两个典型复杂应用对该方法的有效性和稳定性进行了全面验证,包括考虑温度、湿度、飞行高度和马赫数不确定的经典音爆多源不确定量化,以及考虑加工误差和飞行状态参数不确定的跨音速翼型复杂流场不确定量化等.结果均显示,基于FAFBS的PC方法获得了最快的误差收敛率以及最小的近似误差,基于LAR的PC方法的收敛率显著慢于基于FAFBS的PC方法,而原始的全PC方法收敛最慢.并相对于直接使用蒙特卡罗模拟方法进行不确定分析,使用基于FAFBS的PC方法在达到相同矩估计准确率时,计算花费减少3个数量级,可完全满足高效飞行器复杂流场/声爆多源不确定量化以及多学科稳健设计需求.

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.