Reduced order model based on machine learning with sindy autoencoders

Abstract

This work presents a numerical methodology to obtain a reduced order model – ROM – of a linear time-invariant aeroelastic model. The airfoil section of the aeroelastic model, considering only the pitch–plunge motion is studied in a fluid-structure interaction scheme using Computational Fluid Dynamics – CFD. The structural parameters of the linear mechanical system and the necessary data are taken from COMSOL Multiphysics®. In a first analysis, it is shown what is most common in current ROM approaches, a Deep Neural Network - DNN. Such a concept has a high predictive capacity, however, it becomes unfeasible for interpretation and extrapolation of the equations. The Sparse Identification of Nonlinear Dynamics – SINDy – methodology is presented. In order to show the details of the proposed technique, the SINDy technique is implemented in a sparse identification algorithm, Chaotic Lorenz system. Finally, the SINDy methodology is applied to the case of the proposed aeroelastic model. It was possible to identify the system and discover their equations with high accuracy.