结合半参数方法和贝叶斯抽样技术的多响应优化设计

Multi-response optimization design based on semi-parametric methods and Bayesian sampling techniques

响应曲面模型的构建对多响应优化设计结果的影响至关重要.传统的响应曲面模型会事先对模型结构做出一系列的假设.然而,在面向复杂产品的质量设计时往往会出现模型结构错误设定的情况.结合半参数方法和贝叶斯抽样技术提出了一种新的多响应优化设计方法,以解决多目标之间的冲突、模型结构的不确定以及预测响应值的波动性问题.首先,利用半参数方法建立可控因子与响应之间的响应曲面模型;其次,基于贝叶斯抽样技术对模型误差进行修正,建立基于误差修正的响应曲面模型,并在此基础上构建多目标优化函数;然后,利用混合遗传算法进行寻优,获得最佳的参数设计值.另外,基于贝叶斯抽样技术对优化结果进行稳健性评估,以考察优化结果的可靠性.最后,通过一个案例分析说明所提方法的有效性.结果表明,所提方法能有效地解决模型结构不确定以及小样本数据对研究结果的影响,获得更加稳健可靠的优化结果.

Constructing an accurate response surface model is critical to achieving reliable experimental results.Traditional methods tend to make a series of assumptions about the model structure before model fitting.However,misspecification of the model structure often occurs in the quality design of complex products.This paper proposes a new multi-response optimal design method to address the conflicts between multi-objectives,the model structure uncertainty,and the volatility of the response.Firstly,a semi-parametric method is used to establish a response surface model.Secondly,the model error is corrected based on Bayesian sampling technology.Thirdly,a multi-objective optimization function is constructed,and a hybrid genetic algorithm is used to obtain the optimal setting.Finally,a case study is used to illustrate the effectiveness of the proposed method.The results show that the proposed method can effectively solve the model structure uncertainty and the influence of small samples.