Surrogate models and mixtures of experts in aerodynamic performance prediction for aircraft mission analysis

Abstract

The accurate evaluation of aircraft fuel burn over a complete mission is computationally expensive and may require millions of aerodynamic performance evaluations. Thus, it is advantageous to use surrogate models as approximations of high-fidelity aerodynamic or aerostructural models. Conventional surrogate models, such as the radial basis function and kriging, cannot model these functions accurately, especially in the transonic regime. To address this issue, we explore several ways to improve the accuracy of surrogate models. First, we employ an adaptive sampling algorithm to complement a traditional space-filling algorithm. Second, we improve the kriging surrogate performance by including gradient information in the interpolation (a form of gradient-enhanced kriging—GEK) and by introducing a known trend in the global model component (kriging with a trend). Lastly, we propose a mixture of experts (ME) approach, which is based on the divide-and-conquer principle. We validate our surrogate models using aerodynamic data for conventional and unconventional aircraft configurations, and we assess their performance in predicting the mission ranges by analyzing ten mission profiles. Our results show that the proposed ME approach is superior to the traditional models. Using a mixture of GEK models to approximate the drag coefficients gives approximation errors of less than 5% with fewer than 150 samples, whereas the adaptive sampling fails to converge when training a global model. However, when we have a simple function profile, such as the lift and moment coefficients, using a conventional surrogate model is more efficient than an ME model, because of the added computational complexity in the latter. The range estimation errors associated with the ME models are less than 2% for all the benchmark mission profiles considered, whereas some traditional models yield errors as high as 20–80%. We thus conclude that the ME technique is both necessary and sufficient for modeling the aerodynamic coefficients for surrogate-based mission analysis.