Predicting Whirl Flutter Bifurcations Using Machine Learning

This paper investigates the feasibility of using machine learning to predict whirl flutter bifurcation diagrams. The machine learning techniques selected for the study are XGBoost and the long short-term memory neural network. These techniques are selected for their suitability for sequential and nonlinear data. The techniques are investigated for a propeller-nacelle test case with polynomial structural nonlinearities resulting in supercritical or subcritical whirl limit-cycle oscillations. The techniques are trained to learn the bifurcation diagram for the amplitude variation of pitch angle limit-cycle oscillations of the propeller-nacelle system as a function of the forward speed for various levels of cubic structural nonlinearity. Bifurcation diagram learning and testing data are generated using the bifurcation forecasting method. XGBoost is computationally faster to train but less accurate for low amounts of learning data, especially for the most weakly and strongly nonlinear cases. The long short-term memory neural network is more computationally expensive to train but shows a less scattered error pattern for sparse learning data. However, it is sensitive to the amplitude resolution of the bifurcation diagrams. The approach to sample the cubic nonlinearity range does not significantly impact the results once the techniques have a sufficient amount of data to learn from. The data requirements observed in the study suggest that, for these techniques, direct learning of bifurcation diagrams may not scale beyond a handful of input parameters.