快速反射镜椭圆弧柔性铰链多目标优化设计

在快速反射镜柔性铰链优化设计中，为保障反射镜精度和稳定性，应尽量提高柔性铰链工作轴转动柔度和非工作轴转动刚度。以某快速反射镜的椭圆弧柔性铰链为研究对象，首先利用最小二乘法和积分思想推导了三个转动轴的转动柔度公式，与有限元法对比，二者最大相对误差小于6.8%，解决了矩形截面扭转柔度积分过于复杂的问题；其次基于改进的非支配排序遗传算法（NSGA-II）对三个转动轴进行了多目标优化设计，达到设计指标，所得最优解和求解效率较传统算法有了明显提高，其中Pareto解求解效率较多岛遗传算法(MIGA)提高了14.3%，较粒子群算法(PSO)提高了25%；最后对NSGA-II算法所得最优解进行了有限元验证，结果表明二者最大相对误差小于6.5%，吻合较好。

Multi-objective optimal design of elliptic flexible hinge in fast steering mirror

In the optimization design of the flexible hinge in the fast steering mirror, in order to ensure the accuracy and stability, the rotational flexibility of the working axis and the rotational rigidity of the non-working axis should be increased as much as possible. Taking the elliptic arc flexible hinge in a fast steering mirror as the research object, firstly the least squares method and the integral method were used to derive the flexibility formula of three rotation axes. Compared with the Finite Element Analysis (FEA), the relative error was less than 6.8%, the problem of complex integration calculation in torsional flexibility of rectangular section was solved. Secondly, based on the improved non-dominated sorting genetic algorithm (NSGA-II) algorithm, the elliptic flexible hinge was multi-objectively optimized, met the design target and the optimal solution and solution were efficiency improved significantly. The efficiency of Pareto solution was improved by 14.3% compared with the Multi-Island Genetic Algorithm (MIGA) method, and improved by 25% compared with Particle Swarm Optimization (PSO). Finally, the optimization results were verified by FEA. The relative error was less than 6.5%, which was a good agreement.