Development of a low-cost computing method for static aeroelasticity and deep dynamical modeling for unsteady FSI

This study develops a new type of partitioned method for static aeroelasticity of the aircraft wing and models unsteady FSI of the two-dimensional vortex-induced vibration cylinder using a deep autoencoder that includes Koopman operator.

The proposed method has two procedures for figuring out the equilibrium wing deformation. Before computing static aeroelasticity, the method initially assumes deformations based on a few parameters. After the wings are set, the fluid and structure analyses are computed for each deformed wing, and the residual forces are defined by the fluid and structural forces on the wing surfaces. In the subsequent step, the proposed method identifies the minimum residual point, which corresponds to the equilibrium point in the static aeroelasticity analysis of the aircraft wing. The deformations computed by the proposed method matched those of the conventional method (Block Gauss-Seidel method, BGS). In addition, the calculation time was ten times shorter than the BGS, in the best case.

Furthermore, the autoencoder performing as a Koopman function models the dynamics of a two-dimensional flow field surrounding a spring-connected oscillating cylinder. The autoencoder contains residual blocks and was trained using the results of the unsteady fluid-structure interaction analysis as the ground truth. The trained architecture assists in the creation of the system and input matrices of the state equation in control theory, and this equation functions as a reduced order model (ROM) of the unsteady FSI.

The reduced order model reconstructed the ground truth data. Using this reduced order model, a new type of partitioned method for unsteady FSI is currently being developed. These works contribute to the acceleration of FSI analysis computing.

This work was supported by JST SPRING Grant Number JPMJSP2114 and the establishment of university fellowships towards the creation of science technology innovation Grant Number JPMJF2102.