考虑随机型不确定性的浸入式颤振求解方法

Intrusive Flutter Solutions with Stochastic Uncertainty

气动弹性模型中的参数不确定性一般具有一定的分布规律,为了定量分析随机型参数不确定性对颤振的影响特性,考虑气动弹性系统中广义刚度的随机型不确定性,基于浸入式随机多项式展开(PCE)方法,在传统的颤振求解方法——p-k法的基础上,提出了针对不确定性气动弹性系统稳定性分析的增广p-k法——PCEPK(Polynomial Chaos Expansion with p-k)法,并将该方法应用到某机翼的颤振分析中,研究了均匀分布下的广义刚度不确定性对颤振边界的影响,并同基于结构奇异值μ理论的鲁棒颤振分析的结果和计算效率进行了对比。最后,采用标准的蒙特卡罗模拟(Monte Carlo Simulation,MCS)方法验证了结果的正确性。研究结果表明,PCEPK法计算的颤振边界范围是该分布下的"确定"结果,不因随机样本数而改变,克服了随机方法依赖样本数的缺点。同时,与基于结构奇异值理论的鲁棒颤振分析方法相比,它能够考虑不确定性参数分布对颤振特性的影响,具有更广泛的适用范围。

There is generally a certain distribution for parameter uncertainty in an aeroelastic model.In order to quantify the influence of stochastic uncertain parameters on the flutter boundary,a flutter analysis with generalized stiffness stochastic uncertainty is conducted in this work,based on the intrusive polynomial chaos expansion （PCE） theory.According to the traditional flutter solution method,namely the p-k method,an augmented PCEPK （polynomial chaos expansion with p-k） method for an uncertain aeroelastic system is presented to analyze its aeroelastic stability range.This flutter uncertainty analysis method is applied to a wing model,considering structural uncertainties with uniform distribution.A comparison of accuracy and computational time indicates that the range of flutter velocity by the PCEPK method is consistent with that obtained by the robust μ method.Finally,the standard Monte Carlo simulation （MCS） are employed to validate the results of the PCEPK method.In addition,though the parameter uncertainty is stochastic,the flutter velocity range is deterministic,invariant with the sample number,which resists the dependence on the random samples by the usual stochastic method.Moreover,the influence of the different distribution types of parameter uncertainty on flutter boundary can be obtained by the PCEPK method,which is more applicable when compared with the robust flutter analysis with μ method.