Fast flutter evaluation of very flexible wing using interpolation on an optimal training dataset

Abstract

Machine learning strategies can be efficiently used to accelerate the exploration of the design space or flight envelope of highly flexible aeroelastic systems. In this paper, we explore the use of interpolation between parametric state-space realizations to, with few true systems sampled in the parameter space, produce with adequate accuracy a state-space model anywhere in the parameter space. The location of the sampling points is shown to be decisive thus the selection of these points takes the focus in this work. Several approaches are explored, putting emphasis on adaptive schemes that locate the optimal points in the parameter space that are needed to capture the changing system dynamics. Since the evaluation of the true system is costly, optimization techniques based on statistical surrogate models are sought, which need to be trained but are effective in locating the best locations to use as sampling data. A novel method inspired by Bayesian optimization is used to make the most out of a limited number of known state-spaces by taking different combinations as training and testing data of the statistical surrogate, leading to not only an accurate interpolation framework but also to a reduction of 50% of the number of costly full system evaluations compared to a standard Bayesian optimization set-up. These methods are demonstrated on the Pazy wing, a very flexible wing with a complex stability envelope, whereby we produce a very accurate representation of the flutter envelope at a reduced computational cost.

Adaptive Sampling for Interpolation of Reduced-Order Aeroelastic Systems

“…The interpolation framework is not complete without a defined parameter space sampling strategy, and indeed, without adequate sampling the results from the interpolation can be either physically meaningless or computationally intractable for a large parameter space. The examples shown in [68] illustrate the significant sensitivity of the interpolation scheme to the choice of training sets that has inspired the search for algorithms select training points in the parameter space that minimize the interpolation error.…”

“…The limiting factor of this scheme is the large number of evaluations of the true system (which are the ones that this entire work aims to minimize) that are used as testing data only in order to generate 𝜇 𝜀 , not making it onto the training set and thus not being used to improve the interpolation accuracy. As with any regression that depends on testing and training data, it is clear that the sweet-spot lies in a careful balance between the two and in the applications tested with the BO scheme [68], a large number of testing points are required in 𝑃 𝑠 to find 𝑍 0 that are then not later used, thus the scheme is effective albeit inefficient. Consequently, the large number of unused data points has inspired and encouraged the development of our proposed "data-green" sampling strategy, which aims to reuse and recycle a set of the computed points as training and testing sets in order to obtain a more informed Gaussian regression with the same number of full system evaluations.…”