Optimal Sparsity in Nonlinear Non-Parametric Reduced Order Models for Transonic Aeroelastic Systems

Machine learning and artificial intelligence algorithms typically require large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden associated with generating data, usability of such methods has been limited to highly simplified aeroelastic systems. This paper presents a novel approach for the identification of optimized sparse higher-order polynomial-based aeroelastic reduced order models (ROM) to significantly reduce the amount of training data needed without sacrificing fidelity. Several sparsity promoting algorithms are considered, including; rigid sparsity, LASSO regression, and Orthogonal Matching Pursuit (OMP). The study demonstrates that through OMP, it is possible to efficiently identify optimized s-sparse nonlinear aerodynamic ROMs using only aerodynamic response information. This approach is exemplified in a three-dimensional aeroelastic stabilator model experiencing high amplitude freeplay-induced limit cycles. The comparison shows excellent agreement between the ROM and the full-order aeroelastic response, including the ability to generalize to new freeplay and velocity index values, with online computational savings of several orders of magnitude. The development of an Optimally Sparse ROM (OS-ROM) extends previous higher-order polynomial-based ROM approaches for feasible application to complex three-dimensional nonlinear aeroelastic problems, without incurring significant computational burdens or loss of accuracy.