Fuzzy Approximation by a Novel Levenberg–Marquardt Method for Two-Degree-of-Freedom Hypersonic Flutter Model

Abstract

The two-degree-of-freedom (2DOF) hypersonic flutter dynamical system has strong aeroelastic nonlinearities, and it is very difficult to obtain a more precise mathematical model. By considering varying learning rate and σ-modification factor, a novel Levenberg– Marquardt (L–M) method is proposed, based on which, an online fuzzy approximation scheme for 2DOF hypersonic flutter model is established without any human knowledge. Compared with the standard L–M method, the proposed method can obtain faster converge speed and avoid parameter drift. Numerical simulations approve the advantages of the proposed scheme.

Dynamic damage analysis of airfoil flutter for a generic hypersonic flight vehicle

“…It should be noted that the proposed airfoil motion model equations (1)–(2) are different from the results in Zheng and Yang (2008), Zhou et al. (2013), and Wang et al. (2014); that is because ΔL and Δm are considered here, which are the quasi-steady aerodynamic lift and moment increments caused by the flight dynamics, respectively.…”

“…To obtain the damage caused by airfoil flutter, a more precise airfoil motion model should be provided first. Without loss of generality, the airfoil motion model of a generic HFV (Abbas et al., 2008; McNamara and Friedmann, 2011; Wang et al., 2014) is simplified as a two degrees of freedom (2-DOF) airfoil with cubic structure nonlinearity and aerodynamics nonlinearity as presented in Figure 1 (Lee and Singh, 2018).

Figure 1.The sketch of the two-dimensional airfoil system.

…”

“…In Zheng and Yang (2008), Zhou et al. (2013), and Wang et al. (2014), the airfoil motion models only consider the aircrafts flight velocity, and other flight dynamics are not involved in those analyses.…”

“…The flight conditions are: H=30km, α0=1∘, and X(0)=[0.01000]T. According to the results in Zheng and Yang (2008) and Wang et al. (2014), the values of other parameters mentioned above are given in Table 1.…”

“…Airfoil flutter, caused by the mutual interaction of the elastic, inertial, and unsteady aerodynamic forces, is a challenging and important issue in the field of aircraft design due to its potential threat to flight safety (McNamara and Friedmann, 2007, 2011; Wang et al., 2014; Lafontaine et al., 2016; Baghdasaryan et al., 2017). For an aircraft, the airfoil is a crucial component because it contributes most of the lift to the aircraft.…”