Model order reduction for nonlinear aeroelastic dynamical system using automatic differentiation

ifasd2024 Tracking Number 168

One means towards reducing the emissions outputs of the aviation industry is by increasing wing aspect ratio, thus increasing aerodynamic efficiency. This however results in highly flexible lifting surfaces. As part of the aircraft design process, it is necessary to understand the dynamics of these highly flexible lifting surfaces to gust excitation. This may be as part of verifying structural limits are not exceeded – via a worst-case gust search, or, to design control laws for gust alleviation. Performing either of these tasks via direct time integration of the full-order model (FOM) may prove to be computationally intractable. Use of explicit integration schemes with the high-dimensional, nonlinear FOM requires the resolution of impractically small steps-sizes, whilst use of implicit schemes comes with additional computational complexities for nonlinear systems. Thus, there exists the motivation for nonlinear Model Order Reduction (MOR) to reduce system size and computational complexity, while retaining the critical dynamical properties of the system. In Ref. [1] a MOR algorithm for application to flexible aircraft control design was formulated. The approach is based on the eigenspectrum of the FOM Jacobian matrix, projecting a Taylor Series expansion of the original system onto a representative basis of eigenvectors, thus reducing the state-space dimension, and retaining only critical frequency content. In the work of Ref. [1], reduced order nonlinear terms were approximated via Finite Differencing (FD). This method was further developed in Ref. [2], introducing Automatic Differentiation (AD) to overcome round-off and/or truncation errors associated with approximating the reduced order nonlinear terms via FD. This work builds on the method of Ref. [2], presenting a framework to build nonlinear aeroelastic ROM systems using source-transformation AD. Within this work, a study is performed to determine the significance of retaining specific aeroelastic modes in the construction of the nonlinear ROM system. Aeroelastic mode-tracking Ref. [3] is used to assist in determining the physical phenomenon these modes represent by solving eigenvalue problems over varying parameter ranges. This permits mode identification specifically as structural mode shapes, aerodynamic mode shapes or gust-related mode shapes. [1] A. Da Ronch, K. J. Badcock, Y Wang, A. Wynn, and R. Palacios, “Nonlinear Model Reduction for Flexible Aircraft Control Design,” in: AIAA Flight Mechanics Conference, 2012. [2] D. Massegur, D. Clifford, A. Da Ronch, and S. Symon, “Comparing Reduced Order Models for Nonlinear Dynamical Systems,” in: 33rd Congress of the International Council of the Aeronautical Sciences, September 2022. [3] X. Hang, Q. Fei, W. Su, “On Tracking Aeroelastic Modes in Stability Analysis Using Left and Right Eigenvectors”, AIAA Journal, 2019