Quantification analysis of uncertain flutter risks

This article presents a preliminary method of probabilistic robust flutter analysis subject to small flutter risks. This method incorporates robust flutter analysis and probabilistic flutter analysis and is able to provide comprehensive insight into the flutter margin for different levels of risk and uncertainty to support more reasonable decision-making. In robust flutter analysis, the robust critical flutter velocity with zero risk is obtained by the structured singular value (μ) analysis and eigenvalue solution based on the modal iterative method. The probabilistic distribution of flutter velocity and probabilistic critical velocity are estimated by the standard Monte Carlo simulation (MCS) method in probabilistic flutter analysis for large risks. Probability comparison and bisection algorithm are applied to calculate the uncertainty radius and critical velocity of probabilistic robust flutter. The stochastic method with the sample reuse algorithm is also performed to obtain the quantitative relation of risk and uncertainty radius. By considering the mass uncertainty, the above methods are employed to the flutter analysis of a large aspect ratio wing with two spars. The results demonstrate that the deterministic μ method can only be used to zero risk flutter analysis while the standard MCS method is suitable just for large risk flutter analysis. The results of the probabilistic robust flutter analysis show that with 1% increment of flutter risk, the uncertainty radius can be increased by 62% or the flutter velocity can be increased by 5%. Therefore, the design requirement can be adjusted accordingly.