系统工程与电子技术

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基于模型不确定性的响应曲面建模

欧阳林寒, 马义中, 汪建均, 刘健   

  1. 南京理工大学经济管理学院, 江苏 南京 210094
  • 出版日期:2015-07-24 发布日期:2010-01-03

Response surface modeling based on model uncertainty

OUYANG Lin-han, MA Yi-zhong, WANG Jian-jun, LIU Jian   

  1. School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China
  • Online:2015-07-24 Published:2010-01-03

摘要:

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。

Abstract:

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 uncertainty 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 eliminate the redundant information among surrogates and reduce the number of surrogates contained in the ensemble 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.