A long short-term memory network to forecast aeroelastic responses of an airfoil section with shape memory alloy-based hysteretic springs

Predicting aeroelastic flutter and post-flutter limit cycle oscillations (LCO) in airfoil sections employed with shape memory alloy (SMA) springs is a considerable object due to the strong nonlinearities introduced by SMA superelasticity and the high computational cost of numerical simulations. In this study, the question of data-driven deep learning models can predict aeroelastic responses in SMA-based aeroelastic systems accurately and efficiently is addressed. To do this, a long short-term memory (LSTM) architecture which is a sub-type of (DNN) approach is proposed to model the dynamics of an airfoil section with SMA springs. The LSTM network is trained using time-series data generated from high-fidelity aeroelastic numerical simulations incorporating unsteady aerodynamics and nonlinear SMA constitutive behavior. The novelty of the present work lies in the application of LSTM-based deep learning to predict both flutter and post-flutter LCO responses of SMA-integrated airfoils, which has received limited attention in the existing literature. The results demonstrate that the proposed model accurately predicts the onset of flutter, as well as the amplitude and frequency of LCOs, for various SMA preload conditions. In particular, the superelastic effect of SMA springs is shown to increase flutter speed and suppress unstable oscillations by transforming the flutter response into stable LCOs for sufficiently high mechanical preload levels above 2N. The prediction accuracy, quantified using root mean squared error (RMSE) found as 0.97, confirms the robustness and reliability of the proposed approach. Overall, the developed LSTM framework provides a computationally efficient and accurate tool for simulating and designing aeroelastic systems with SMA components and can be extended to other nonlinear aeroelastic applications.