一种自适应抽样的代理模型构建及其在复材结构优化中的应用
Construction of an adaptive sampling surrogate model and application in composite material structure optimization

提出了基于一种自适应抽样和增强径向基插值的自适应代理模型方法，这种自适应抽样方法以确定适量的样本点数量和提高代理模型自适应能力为目的，使新增样本点位于设计空间的稀疏区域并确保所有的样本点均匀分布于设计空间以提高代理模型精度。标准误差用来判断代理模型的精度大小并决定是否对代理模型进行更新。一种条件随机抽样被用来对比本文的自适应抽样方法。经过对比验证发现，采用自适应抽样方法的代理模型精度比条件随机抽样方法的代理模型精度高。这种自适应代理模型结合多岛遗传算法被用来优化旋翼臂的碳纤维增强环氧树脂复合材料铺层角度使得旋翼臂的一阶模态频率最大。优化结果表明，不同的碳纤维增强环氧树脂复合材料铺层角度对旋翼臂的一阶模态频率值影响较大，优化结果获取了最优铺层角度，旋翼臂的一阶模态频率值被提高以远离激励频率而避免旋翼飞机的共振。 An adaptive surrogate model was proposed using an adaptive sampling and enhanced radial basis function(ERBF). The adaptive sampling method was used to determine the appropriate number of sample points and to improve the adaptive capacity of the surrogate model. New sampling points were located in sparse areas and ensure that all sample points were evenly distributed in the design space to improve the accuracy of the surrogate model. The standard error was used to determine the accuracy of the surrogate model and to determine whether the surrogate model was updated. A conditional random sampling was used to compare the adaptive sampling methods in this paper. It is found that the accuracy of the surrogate model with adaptive sampling method is higher than that of the conditional random sampling method. This adaptive surrogate model is combined with the multi-island genetic algorithm to optimize the fiber angle of carbon fiber reinforced epoxy resin composites for the rotor-arm and obtain the highest first-order modal value of the rotor-arm. The optimization results show that the fiber angle of carbon fiber reinforced epoxy resin composites has a great influence on the first-order modal value of the rotor-arm. The optimization result obtains the optimum layer angles, and the first-order modal value of the rotor-arm is kept away from the rotation frequency to prevent resonance. 江苏省自然科学基金（BK20160817）；中央高校基本科研基金（30915118807；30917011302）