Bayesian hierarchical modelling for process optimisation

Abstract

Many industrial process optimisation methods rely on empirical models that relate output responses to a set of design variables. One of the most crucial problems in process optimisation is how to efficiently implement model selection and model estimation. This paper presents a Bayesian hierarchical modelling approach to process optimisation based on the seemingly unrelated regression (SUR) models. This approach can estimate a set of predictors to be included in a model based on a Bayesian hierarchical procedure (i.e. model selection) and then give model prediction based on a Bayesian SUR model (i.e. model estimation). Meanwhile, a two-stage optimisation strategy considering practitioners’ preference information is proposed in process optimisation, which initially finds a set of non-dominated input settings and then determines the best one based on the similarity to an ideal solution method. The performance and effectiveness of the proposed method are illustrated with both simulation studies and a case study. The comparison results demonstrate that the proposed method can be a good alternative to existing process optimisation methods.

Keywords:

• Response surface methodology
• Bayesian hierarchical modelling
• model selection and estimation
• SUR models
• process optimisation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (Grant Numbers 71931006, 71702072, 71871119), the Fundamental Research Funds for the Central Universities (Grant Number NR2019002), the Natural Science Foundation for Jiangsu Institutions (Grant Number BK20170810), and the international cooperation program managed by the National Research Foundation of Korea (Grant Number 2018K2A9A2A06019662), the China Postdoctoral Science Foundation (Grant Number 2019T120429).