Reliability-based aeroelastic design of composite plate wings using a stability margin

Reliability-based design is concerned with ensuring that constraints are enforced with acceptable probability under inherent variability in properties. In aircraft design, such a constraint may be that aeroelastic instability does not occur at velocities encountered by the aircraft. This approach can be complicated, as the aeroelastic instability speed is a discontinuous function of material properties, on account of particular modes only becoming unstable for some parameter values. In reliability analysis, it is common to use surrogate models due to the computational expense associated with Monte Carlo Simulation, however, such methods can be inaccurate when emulating discontinuous functions such as the aeroelastic instability speed. In this paper, an alternative approach is proposed in which Gaussian process surrogate models are fitted directly to each of the modal eigenvalues at the design air-speed, and used to emulate a stability margin based upon the most critical eigenvalue. Using this approach, it is shown that the reliability may be estimated for the aeroelastic stability using smooth emulators, thereby overcoming the problems associated with discontinuities.
The method is demonstrated for layup optimisation of composite plate wings with uncertain ply angles, in which the probability of aeroelastic instability occurring is minimised for a prescribed air-speed. In uncertainty quantification,
a good agreement is found with Monte Carlo Simulation with an order of two magnitudes reduction in model runs. Through reliability-based design, reductions in the probability of failure of up to 99.8% are achieved by increasing
the stability margin at the design speed.