基于模型不确定性的响应曲面建模

Response surface modeling based on model uncertainty

针对响应曲面构建中模型不确定性问题,在组合建模方法的基础上,通过引入包容性检验,提出了基于包容性检验的稳健性组合建模方法(ensemble of surrogates based on encompassing test,ET-EOS)。首先,根据实际问题及各模型的特点确定子模型集,进而构建各子模型;其次,采用包容性检验筛选子模型,以消除子模型间存在的冗余信息;然后对筛选出的子模型进行加权组合,以构建ET-EOS模型。基于包容性检验,提出了稳健的组合模型,解决了模型不确定下的响应曲面构建问题。最后,结合实际案例和仿真试验验证提出方法的有效性,结果表明此方法不仅改善了模型的预测性能及其稳健性能,而且通过筛选子模型减少了建模所需的工作量。

In most engineering problems, model uncertainty is inevitably involved in the robust parameter design. Ensemble of surrogates based on the encompassing test （ET-EOS） is proposed to consider model uncer- tainty for response surface modeling. Firstly, sub-surrogates are assured according to the practical problem and characteristics of models, then different surrogates are constructed. Secondly, encompassing tests are used to e- liminate the redundant information among surrogates and reduce the number of surrogates contained in the en- semble of surrogates, and then the effective sub-surrogates are identified. Weighted average for all models is carried out to obtain a robust ensemble model. Finally, the effectiveness of the proposed method is verified through a practical industrial example combined with a simulation example. The results reveal that the proposed method not only improves the prediction and the robustness of model prediction, but also reduce the computing cost for constructing models.