最优阶次多项式响应面法及其在模型修正中的应用

Construction of Response Surface with Optimal Order Polynomial and Its Application in FEM Updating

提出一种构造最优阶次多项式响应面方法,通过多元回归分析参数对响应不同阶次下的拟合精度与显著度,建立判断多项式各参数最优拟合阶次的方法,解决了常规多项式响应面法中阶次固定且统一的限制,提升了代理模型的精度。将响应面法应用于有限元模型修正中,建立基于最优阶次响应面法有限元模型修正的理论框架,提高了修正的效率,并保证了修正后模型的精度。以功能函数为例,验证了最优阶次多项式响应面法可实现更高精度的模型替代。以GARTEUR飞机的实测模态修正初始有限元模型,阐述了响应面构建以及模型修正的过程,并有效修正了初始模型误差,减少了经典模型修正迭代中调用有限元软件计算灵敏度的时间,证明了最优阶次多项式响应面可成功应用于有限元模型修正中。

A method of constructing the optimal order polynomial response surface is proposed.By analyzing the fitting accuracy and significance of the analysis parameters to the response of different orders through multiple regression,a method to determine the optimal fitting order of each parameter of the polynomial is established.The fixed and uniform restrictions in the conventional polynomial response surface method are solved,and the accuracy of the proxy model is improved.The RSM is applied to the FEM updating,and the theory of the FEM updating based on the optimal order RSM is established,which improves the efficiency and the accuracy.With the functional function as an example,it is verified that the optimal polynomial RSM can realize the model substitution with higher accuracy.Taking the GARTEUR aircraft as an example to correct the initial FEM by the measured modal,the process of response surface construction and model updating is described,the initial model error is corrected effectively,and the sensitivity calculation time of the finite element software during the classical model correction iteration is reduced,which proves that the optimal polynomial response surface can be successfully applied to the FEM updating.