The reliability of a pitch-plunge hypersonic airfoil in random fluctuating flow with both cubic and freeplay nonlinearity is examined. The Hopf bifurcation and dynamic responses of the hypersonic airfoil are performed. To analyze the reliability, the effects of stochasticity on the dynamic behaviors of the hypersonic airfoil model are discussed in detail. Several unwanted phenomena that result in the failure of the airfoil structure are induced by random fluctuations. Subsequently, the reliability of the airfoil model is defined and analyzed according to the first passage failure criteria. The effects of different parameters on the reliability are investigated. Furthermore, a nonlinear energy sink is introduced to suppress the vibration of the airfoil and enhance the reliability. Two-dimensional reliability regions of the airfoil model are given to provide the safety parameter region. The results show that the reliability of the airfoil model is significantly improved with the nonlinear energy sink. This work will provide new insights into the safety design of hypersonic aircraft.

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 [ ] and smoothed [ ] 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 [ ] 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.