In this paper, a new approach for multi-objective robust optimization of flutter velocity and maximum displacement of the wing tip are investigated. The wing is under the influence of bending–torsion coupling and its design variables have different levels of uncertainty. In designing and optimizing wings with a high aspect ratio, the optimization process can be done in such a way to increase the flutter velocity, but this can increase the amplitude of the wing tip displacement to a point that leads to the wings damage and structural failure. Therefore, single-objective design optimization may lead to infeasible designs. Thus, for multi-objective optimization, modeling is based on the Euler–Bernoulli cantilever beam model in quasi-steady aerodynamic condition. Using the Galerkin’s techniques, the aeroelastic equations are converted to ODE equations. After validating the results, the system time response is obtained by the numerical solution of the governing equations using 4th Runge–Kutta method and the flutter velocity of the wing is obtained using the theory of eigenvalues. Subsequently, by choosing bending and torsional rigidity and mass per unit wing length as the optimization variables, using Monte Carlo–Latin hypercube (MC-LH) simulation and 4th polynomial chaos expansion (PCE), the effect of uncertainty on these variables is modeled in modeFRONTIER™ software coupled with MATLAB™ and optimization is performed by genetic algorithm. Finally, by plotting the Pareto front, it is observed that with an acceptable increase in flutter velocity, the maximum wing displacement amplitude is reduced as much as possible. The results of the multi-objective robust optimization show more feasible results compared with deterministic optimization.

本文研究了一种新的多目标鲁棒速度和翼尖最大位移鲁棒优化方法。机翼受弯扭耦合的影响，其设计变量具有不同程度的不确定性。在设计和优化具有高长宽比的机翼时，可以以提高颤振速度的方式完成优化过程，但这可能会使机翼尖端位移的幅度增加到导致机翼损坏和结构破坏的程度。因此，单目标设计优化可能会导致不可行的设计。因此，对于多目标优化，建模是基于准稳态空气动力学条件下的Euler–Bernoulli悬臂梁模型。使用Galerkin的技术，将空气弹性方程转换为ODE方程。验证结果后，使用第四次Runge-Kutta方法通过控制方程的数值解获得系统时间响应，并使用特征值理论获得机翼的扑动速度。随后，通过选择弯曲和扭转刚度以及单位机翼长度的质量作为最优化变量，使用蒙特卡洛-拉丁超立方体（MC-LH）模拟和四次多项式混沌扩展（PCE），将不确定性对这些变量的影响建模为结合了MATLAB™的modeFRONTIER™软件和优化是通过遗传算法执行的。最后，通过绘制帕累托锋线，可以观察到随着颤动速度的增加，最大机翼位移幅度将尽可能减小。