Reduced-Order Modeling of Unsteady Aerodynamics Using Constrained Optimization and Random Input

This work proposes a data-driven methodology for identifying unsteady aerodynamic reduced-order models (ROM) for flexible structures in freestream flow. The method utilizes constrained gradient-based optimization to extract aerodynamic stiffness, damping, and time-domain convolution kernels from input-output data. To efficiently generate the training dataset from a single computational fluid dynamics simulation, the fluid is excited using simultaneous band-limited white noise in all structural modal coordinates. Unlike traditional least-squares identification techniques, which suffer from numerical instability and high memory requirements when applied to high-dimensional systems or long memory kernels, the proposed optimization framework is iterative and inversion-free. The loss function incorporates physics-informed regularization terms to enforce kernel smoothness and temporal decay. The approach is implemented in PyTorch and validated against Linear Potential Flow theory and inviscid Euler simulations for a clamped elastic panel in supersonic flow (Mach 1.2 to 1.94). The effects of training data time step, simulation length, and random excitation bandwidth on ROM accuracy are investigated. The results demonstrate that the identified ROMs accurately predict flutter onset and the properties of the post-flutter limit-cycle oscillation. Furthermore, the method demonstrates superior scalability by successfully identifying a 16-degree-of-freedom model with approximately 50,000 parameters, a case where the classical least-squares approach failed to converge.