On the use of feed-forward neural networks in the context of surrogate aeroelastic simulations

Abstract

For a few decades now, the proliferation of digital computers has driven the development of increasingly complex models to study the physical phenomena that are part of our reality. Particularly, in the field of aeronautics and renewable energy (wind), correct aeroelastic modeling is crucial for many reasons: structural and aerodynamic optimization, determining operational envelopes, and avoiding destructive aeroelastic phenomena such as divergence or flutter, among others. Furthermore, the study of systems involving multiple fields of physics (aerodynamics, structural dynamics, control, etc.) is characterized by exhibiting highly nonlinear phenomena (limit cycle oscillations, bifurcations, chaos, etc.), which are very challenging to capture with linear approximations or simplified models. In this work, we present a comprehensive statistical analysis of the performance of shallow feed-forward neural networks (FNNs) to capture supercritical Hopf bifurcations when dealing with aeroelastic flutter. The FNNs are trained by considering data sets generated by using two different aeroelastic models of increasing complexity. For the structural model, we consider a two-degree-of-freedom model consisting of an airfoil oscillating in pitch and plunge. The aerodynamic forces are accounted for by using two different flow solvers: (1) a non-compressible two-dimensional linear (but ergodic) model based on Wagner’s theory (referred as Fung’s model), which results in analytical expressions for the lift and aerodynamic moment, and (2) a two-dimensional version of the well-known unsteady vortex-lattice method (UVLM). The assessment of the resulting FNN-based models is carried out through a Monte Carlo experiment over R replicates. As a measure of performance, we use the mean-squared error test associated with the estimators, here the system’s response and its consistent aerodynamic coefficients. We also discuss, in detail, the behavior of FNN-based surrogate aeroelastic frameworks when they are trained with data coming from Fung-based or UVLM-based aeroelastic simulations. Furthermore, we highlight a number of challenges faced by shallow FNNs, as well as some difficulties when integrated into surrogate aeroelastic environments. Finally, we provide explanations to questions raised throughout the article and conjecture some others without a definitive answer.