Probabilistic Prediction of Coalescence Flutter Using Measurements: Application to the Flutter Margin Method

TL;DR

This paper enhances the Bayesian flutter margin method by incorporating joint priors of modal parameters, improving flutter speed predictions and reducing flight test costs through better uncertainty quantification.

Contribution

It generalizes the Bayesian flutter margin method with joint modal priors, leading to more accurate flutter speed estimates from flight data.

Findings

Significant reduction in uncertainty of flutter speed predictions

Improved accuracy over previous Bayesian methods

Potential to reduce flight testing costs

Abstract

Zimmerman and Weissenburger's flutter margin method is widely used to estimate the aeroelastic coalescence flutter speed. In contrast to aeroelastic decay rates, the flutter margin exhibits monotonic decay with respect to airspeed redering it effective in extrapolating the flutter speed using flight test data conducted at pre-flutter airspeeds. This paper reports the generalization of the Bayesian formulation of the flutter margin method by Khalil et al. developed to tackle measurement and modeling uncertainties. This paper improves the predictive performance of the previous algorithm by incorporating the joint prior of aeroelastic modal frequencies and decay rates among airspeeds in order to better estimate the joint posterior of modal parameters using observational data. The modal parameter prior is constructed using the classical two-degree-of-freedom pitch-plunge aeroelastic model whose system matrices (e.g. structural stiffness and damping matrices) vary randomly. Such joint modal parameter prior enforces statistical dependence among posteriors of modal parameters and the associated flutter margins across airspeeds. Numerical studies demonstrate a considerable reduction of uncertainties on the predicted flutter speed obtained from the generalized Bayesian flutter margin method. This improved algorithm can cut cost by reducing the number of flight tests and better assess the uncertainty against aeroelastic flutter.