稳健优化设计中代理模型不确定性的研究

Robust Design Optimization Considering Metamodel Uncertainty

代理模型的应用解决了稳健设计中计算量大的难题,但由于代理模型与真实模型间存在误差(代理模型的不确定性),而传统的稳健设计忽视了这种不确定性,必然会带来一定的设计误差。因此,针对稳健设计提出了一种基于蒙特卡洛抽样的代理模型不确定性的量化方法,在传统仅考虑参数不确定性的基础上,额外计入代理模型的不确定性对设计的影响。将提出的方法应用于一个数学算例和一个火箭弹卷弧翼气动稳健优化设计,所得优化结果较传统的未考虑代理模型不确定的稳健设计更为精确、合理,证实了提出方法的有效性。

The application of metamodel techniques greatly reduces the computational cost in robust design. However, metamodel is only an approximation of the original model resulting in metamodel uncertainty. In the traditional robust design, only parameter uncertainty is considered rather than metamodel uncertainty, which may induce design error. To address this issue, a method based on Monte Carlo sampling is proposed to quantify the metamodel uncertainty in robust design. With the proposed method, the synthesize effect of both parameter and metamodel uncertainties are quantified. The proposed method is applied to robust design for a numerical example and aerodynamic optimization of rocket wrap-around fins. Compared to the traditional method, the results are more accurate and reasonable, which demonstrates the effectiveness of the proposed method.