Abstract
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.
Highlights
Composite materials are being used to an increasing degree in aerospace structures due to a number of useful attributes including high specific strength and stiffness, and anisotropic behaviour which may be exploited to tailor the properties of the structure
Due to the high computation time associated with reliability-based design, it can be desirable to estimate the probability of failure using surrogate models which may be evaluated in a fraction of the time required by the model itself
A surrogate modelling approach has been presented for use in the reliability-based aeroelastic design of composite wings
Summary
Composite materials are being used to an increasing degree in aerospace structures due to a number of useful attributes including high specific strength and stiffness, and anisotropic behaviour which may be exploited to tailor the properties of the structure. Efficient methods are required in order to account for material uncertainty in the design of composite aircraft wings, subject to objectives or constraints based upon aeroelastic stability. This approach enables the problem to be reformulated from that of approximating a discontinuous function, to that of approximating multiple continuous functions, and exploits the fact that each model evaluation presents an opportunity for surrogate models to ‘learn’ about multiple eigenvalues Using this approach, the reliability may be estimated without the need to partition the input parameter space. The proposed approach is demonstrated in the reliability-based design of a simple composite plate wing model, with uncertainty in the ply orientations. It should, be noted that the surrogate modelling techniques used are entirely non-intrusive, and can be applied to any black-box model. It will in general be simpler to emulate the eigenvalues instead of the instability speed
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