Nonlinear Aeroelastic Reduced Order Modeling with Optimized Sparse Multi-Input Volterra Kernels

Nonlinear unsteady aerodynamic reduced-order models (ROMs) based on machine learning or artificial intelligence algorithms can be complex and computationally demanding to train, meaning that for practical aeroelastic applications, the conservative nature of linearization is often favored. Therefore, there is a requirement for novel nonlinear aeroelastic ROM approaches that are accurate, simple, and, most importantly, efficient to generate. This paper proposes a novel nonlinear unsteady aerodynamic ROM formulated as a highly compact multi-input Volterra series. Orthogonal matching pursuit is used to obtain a set of optimally sparse nonlinear multi-input ROM coefficients from unsteady aerodynamic training data. The framework is exemplified in an aeroelastic setting using the benchmark supercritical wing, considering forced response, flutter, and limit cycle oscillation. The simple and efficient optimal sparsity multi-input ROM framework performs with high accuracy compared to the full-order aeroelastic model, requiring only a fraction of the hundreds of thousands of possible multi-input terms to be identified and allowing a 98% reduction in the number of training samples.