Bayesian hierarchical modelling for process optimisation

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.