系统工程与电子技术 ›› 2018, Vol. 40 ›› Issue (8): 1794-1802.doi: 10.3969/j.issn.1001-506X.2018.08.18

• 系统工程 • 上一篇    下一篇

考虑预测响应值波动的多响应优化设计

汪建均, 屠雅楠   

  1. 南京理工大学经济管理学院, 江苏 南京 210094
  • 出版日期:2018-07-25 发布日期:2018-07-25

Optimal design for multiple responses considering predicted response variability

WANG Jianjun, TU Yanan   

  1. School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China
  • Online:2018-07-25 Published:2018-07-25

摘要:

在多响应优化设计中,模型参数的不确定性以及生产过程的噪声因子不可避免地会导致预测响应值出现较大的波动。针对上述的问题,结合贝叶斯抽样技术、帕累托优化策略以及灰色关联分析方法提出了一种多响应优化设计方法。首先,考虑模型参数的不确定性,运用贝叶斯多元回归模型构建了过程响应与试验因子之间的函数关系;其次,根据帕累托最优策略求出了帕累托最优前沿,并计算各试验点达到帕累托最优的贝叶斯后验概率;然后,利用灰色关联分析方法识别出最佳的优化设计方案;最后,实际案例研究表明,在考虑预测响应值波动时,所提的方法能够获得更为稳健和可靠的优化结果。

Abstract:

In the multi-response optimization design, the model parameter uncertainty and the noise factors in the production process inevitably lead to high fluctuation of the predicted response value. In view of the above problems, a method for multiresponse optimization is proposed based on the Bayesian sampling technique, the Pareto optimization strategy and the grey relational analysis method. Firstly, a Bayesian multiple regression model is used to construct the relationship between the process responses and the experimental factors when considering the uncertainty of the model parameters. Secondly, the Pareto optimality frontier is obtained based on the Pareto optimal strategy, and then the Bayesian posterior probability for experimental points on the Pareto optimality frontier is calculated. Thirdly, the grey relational analysis method is used to identify the optimal design scheme. Finally, a practical example reveals that the proposed method can improve the robustness and the reliability of optimization results when considering the variability of the predicted responses.