A novel long short-term memory neural-network-based self-excited force model of limit cycle oscillations of nonlinear flutter for various aerodynamic configurations

Due to the strong nonlinear properties of the entire flutter process [including growth stages, decay stages and steady limit cycle oscillations (LCOs)], the generalization of the self-excited force model for the entire flutter process of bluff bodies is a very critical issue. This paper proposes a self-excited force model based on a novel long short-term memory (LSTM) neural network to simulate the entire flutter process for various leading-edge configurations. To obtain the dataset, the nonlinear flutter with the growth stages, decay stages and steady LCOs for different leading-edge aerodynamic configurations is investigated by a series of two-degrees-of-freedom spring-suspended sectional model tests. Based on the measured flutter responses and self-excited forces in the tests, a data-driven self-excited force model is proposed on the basis of a novel LSTM neural network. Considering that the nonlinear dynamic system is very sensitive to the accuracy of the model parameters, the Newmark-β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} method is incorporated into the LSTM networks and forms a closed-loop process to restrain the error amplification effects and improve the model robustness, that is, the response calculated from the output of LSTM (the self-excited force) by the Newmark-β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} method is set as the input of LSTM at the next step rather than the measured response. To validate the performance of the proposed model, the flutter critical wind speed, time history of oscillation and self-excited forces, steady-state oscillation amplitude and flutter development process predicted by the model are compared with the test results. The comparison indicates that the predicted results agree well with the test results, meaning that the proposed model has high accuracy, generalization and robustness in describing the nonlinear characteristics of the flutter for various aerodynamic configurations.