In practical engineering, aircraft structures may encounter complex flight environments that can induce intricate stochastic dynamic behaviors, significantly impacting flight safety. However, the analysis of the complex stochastic dynamic behaviors of airfoil structures, especially for fractional viscoelastic systems, is a challenging issue. In this paper, a unified and adaptive approach based on a novel direct probability integral method (DPIM) is proposed to address this challenge. Firstly, the fractional viscoelastic airfoil model under complex flight conditions is established, in which the extreme random flight load is simulated by L & eacute;vy white noise. Then, the probability density integral equation (PDIE) of the fractional viscoelastic airfoil system is derived. Furthermore, the important equivalence between PDIE and Einstein-Smoluchowsky differential equation is demonstrated, exhibiting the superiority of PDIE. To solve PDIE, a fully adaptive DPIM without truncating time is presented. The DPIM-based approach is proposed to achieve the global analysis of fractional viscoelastic airfoil systems. The proposed approach provides a new probabilistic perspective for obtaining the generalized stochastic attractor and basin. Moreover, it fulfills stochastic bifurcation and global analyses of the fractional viscoelastic airfoil model under complex flight environments in a unified way. It is worth noting that as the fractional order increases, the stable region becomes more irregular compared to the effects of extreme random flight loads, leading to a rapid decrease in the probability of stability. The generalized stochastic attractor delineates the region of airfoil movement with high flight stability, and the stability probability can be measured by the generalized stochastic basin.
