Abstract

Empirical models that relate multiple quality features to a set of design variables play a vital role in many industrial process optimization methods. Many of the current modeling methods employ a single-response normal model to analyze industrial processes without taking into consideration the high correlations and the non-normality among the response variables. Also, the problem of variable selection has also not yet been fully investigated within this modeling framework. Failure to account for these issues may result in a misleading prediction model, and therefore, poor process design. In this article, we propose a robust Bayesian seemingly unrelated regression model to simultaneously analyze multiple-feature systems while accounting for the high correlation, non-normality, and variable selection issues. Additionally, we propose a Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full joint posterior distribution to obtain the robust Bayesian estimates. Simulation experiments are executed to investigate the performance of the proposed Bayesian method, which is also illustrated by application to a laser cladding repair process. The analysis results show that the proposed modeling technique compares favorably with its classic counterpart in the literature.

摘要

将多个质量特征与一组设计变量相关联的经验模型在许多工业过程优化方法中起着至关重要的作用。当前的许多建模方法都采用单响应正态模型来分析工业过程，而没有考虑响应变量之间的高相关性和非正态性。此外，变量选择问题也尚未在此建模框架内得到充分研究。不考虑这些问题可能会导致误导性的预测模型，从而导致不良的工艺设计。在本文中，我们提出了一个稳健的贝叶斯看似无关的回归模型，以同时分析多特征系统，同时解决高相关性、非正态性和变量选择问题。此外，我们提出了一种马尔可夫链蒙特卡罗采样算法，从完整的联合后验分布生成后验样本，以获得鲁棒的贝叶斯估计。执行模拟实验以研究所提出的贝叶斯方法的性能，这也通过应用于激光熔覆修复过程来说明。分析结果表明，所提出的建模技术与文献中的经典对应技术相比具有优势。