Quality design based on kernel trick and Bayesian semiparametric model for multi-response processes with complex correlations
针对多响应过程中响应与输入因素间的复杂关系以及响应间的非线性相关性，提出结合核主成分分析、贝叶斯半参数加性模型和进化算法的质量设计方法，并通过仿真和案例验证其建模与优化效果。
Processes or products are typically complex systems with numerous interrelated procedures and interdependent components. This results in complex relationships between responses and input factors, as well as complex nonlinear correlations among multiple responses. If the two types of complex correlations in the quality design cannot be properly dealt with, it will affect the prediction accuracy of the response surface model, as well as the accuracy and reliability of the recommended optimal solutions. In this paper, we combine kernel trick-based kernel principal component analysis, spline-based Bayesian semiparametric additive model, and normal boundary intersection-based evolutionary algorithm to address these two types of complex correlations. The effectiveness of the proposed method in modeling and optimisation is validated through a simulation study and a case study. The results show that the proposed Bayesian semiparametric additive model can better describe the process relationships compared to least squares regression, random forest regression, and support vector basis regression, and the proposed multi-objective optimisation method performs well on several indicators mentioned in the paper.