Physics-Constrained Bayesian ARX for Aeroelastic Flutter Boundary Prediction and Risk-Constrained Speed Increase

Flutter tests approach the instability boundary from the subcritical side, but predicting it from limited subcritical data involves large extrapolation uncertainty and lacks reliability and risk information. A physics-constrained Bayesian ARX method is developed for aeroelastic flutter-boundary prediction. Generalized aerodynamic forces are reconstructed from structural modal equations and represented by a multi-input multi-output ARX model. Instead of deterministic ARX coefficients, model parameters and residual covariance are treated in a matrix-normal–inverse-Wishart conjugate Bayesian framework. Posterior samples are embedded individually into closed-loop aeroelastic state-space equations; eigenvalue analysis yields posterior distributions of flutter speed, credible intervals, conservative quantiles, and instability probability at candidate speeds. The method is validated on the NACA64A010/Isogai two-degree-of-freedom airfoil using multi-speed RMS ratios and logarithmic growth rates as reference. Bayesian ARX retains least-squares ARX reconstruction capability while propagating parameter uncertainty to the flutter boundary; the posterior concentrates as stable data approach the critical region. A numerical three-dimensional wing with control surfaces further demonstrates the full chain from GVT modal data and measured responses through modal projection, aerodynamic-force reconstruction, Bayesian ARX identification, and posterior prediction. The framework quantitatively supports speed-increment selection under an instability-risk constraint. Posterior calibration is verified by credible-interval coverage tests over repeated noisy realizations; the prediction is validated out of sample and against classical damping-extrapolation and flutter-margin methods; and sensitivity studies quantify the effects of model order, prior, measurement noise, record length, and sensor layout. The three-dimensional demonstration is built on a rational-function aerodynamic truth model validated against a p-k benchmark and is framed throughout as a numerical wind-tunnel study.