模型替代方法在优化设计中的应用

Comparison of different metamodeling methods for optimization design

在优化设计问题中,常常会遇到目标响应与设计变量之间具有隐式函数关系的情况.针对此类问题,模型替代方法可以通过寻找输入参数和输出响应之间的转换关系来替代真实未知的目标函数.考虑了响应面法(RSM)、Kriging模型、径向基函数(RBF)神经网络和高阶模型替代法(HDMR)等常见的模型替代方法,对它们的原理、优缺点进行了对比分析.对优化算法进行了改进,提出了截断多初始点搜索优化算法,以期尽可能全面地搜索其全局最优点,为结构设计提供全面的指导.

For the structural optimization design,the relationship between the objective function and design variables is a high nonlinear,and high dimensional implicit function.How to cope with these cases？Metamodeling methods can be used to capture the association patterns between input variables and output response.The response surface method（RSM）,kriging model,radial basis function（RBF）based neural network and high dimensional model representations（HDMR）,are presented,the effectiveness and versatility of those methods are identified by several numerical examples.Metamodeling methods are proposed to apply for optimization design.The optimization algorithm is developed to search all the global minimums by selected multiple initial points.Thus it can provide the guidance for structural design.