基于贝叶斯组合建模的非正态响应稳健参数设计  

Robust Parameter Design for Non-normal Response Based on Bayesian Ensemble Modeling

作　　者：任晓蕾 汪建均[1] 丁春风 翟翠红 REN Xiaoei;WANG Jianjun;DING Chunfeng;ZHAI Cuihong(School of Economics and Management,Nanjing University of Science and Technology,Nanjing,Jiangsu 210094,China)

机构地区：[1]南京理工大学经济管理学院,江苏南京210094

出　　处：《工业工程与管理》2024年第3期115-126,共12页Industrial Engineering and Management

基　　金：国家自然科学基金资助项目(72171118,71931006,71771121);江苏省研究生科研创新计划项目(KYCX22_0498)。

摘　　要：在复杂产品或先进制造过程中往往存在各种影响产品质量设计的不确定性因素,会对模型精度和分析结果产生不利影响。因此,针对模型不确定的非正态响应稳健参数设计问题,提出了一种新的广义线性模型的贝叶斯模型平均方法来解决非正态响应的模型不确定问题。首先,在贝叶斯广义线性模型的框架下纳入变量指示器和模型指示器,利用因子效应原则识别显著效应;其次,通过贝叶斯抽样技术计算变量指示器和模型指示器的后验概率以确定模型权重与模型结构,并利用模拟程序获得模拟响应值;然后,基于模拟响应值构建质量损失函数确定优化方案寻找最优解;最后,通过实际微纳钻孔和3D打印案例证明了该方法的有效性。结果表明,在解决非正态响应下的模型不确定的稳健参数设计中,所提方法与现有方法相比质量损失更低且更加合理稳健。In complex products or advanced manufacturing processes,there are various uncertainties affecting the design of product quality that adversely affect the accuracy of the model,leading to poor parameter design.Therefore,a new Bayesian model averaging method for generalized linear models was proposed to solve the model uncertainty problem of non-normal responses for the robust parameter design problem with model uncertainty.Firstly,the variable indicators and model indicators were incorporated in the framework of the Bayesian generalized linear model to identify significant effects using the factorial effect principle.Secondly,the posterior probabilities of the variable indicators and model indicators were calculated by Bayesian sampling techniques to determine the model weights and model form,and simulated response values were obtained using a simulation procedure.Then,the quality loss function was constructed based on the simulated response values and the optimization scheme was determined in order to find the optimal solution.Then,the quality loss function was constructed based on the simulated response values and the optimization scheme was determined in order to find the optimal solution.Finally,the effectiveness of the method was demonstrated by practical micro-nano drilling and 3D printing cases.The results show that the proposed method in robust parameter design for solving model uncertainty under non-normal response has lower quality loss and is more reasonably robust than existing methods.

关 键 词：模型不确定 稳健参数设计 广义线性模型 贝叶斯模型平均方法 因子效应原则 

分 类 号：TP273.2[自动化与计算机技术—检测技术与自动化装置]