Reconstructing Attractors of a Conceptual Airfoil System via Next Generation Reservoir Computing

Reconstructing attractors of airfoil systems from observations facilitates understanding of aeroelasticity, especially the onset of flutter. However, it is generally difficult due to observation noise and the nonlinear nature of the underlying dynamics. In this study, a hybrid strategy is proposed which incorporates data preprocessing and next generation reservoir computing (NG-RC) for reconstructing attractors of an airfoil system. This approach first estimates the system states from noisy observations via a state estimation method and then trains the NG-RC model to predict the responses of the airfoil system. The NG-RC employs nonlinear functions of past states to approximate the dynamics, requiring less training data and fewer hyperparameters than the conventional reservoir computing. To reduce the model complexity, both L₂ and smoothed L₁ norm penalties are introduced to promote the sparsity of trainable weights, where the optimal weights are determined by simple iterative optimization. Simulation results show that the proposed method can predict various vibration patterns and reconstruct the attractors of the airfoil system from limited, noisy observations. The smoothed L₁ norm penalty can lead to sparser weights and, in some cases, enhance performance. The findings support applications of the present method like flutter boundary prediction and flight accident analysis.