Robust multi-response surface optimisation based on Bayesian quantile model

In robust parameter design, model parameter uncertainty and quality of experimental data often affect the establishment of response surface models, which in turn affect the acquisition of the optimal operating conditions. This paper proposes a robust multi-response surface modelling and optimisation method based on Bayesian quantile regression, which is a robust regression technique insensitive to outliers, to address the above problems. We first incorporate quantile regression into the Bayesian framework and use Bayes's theorem to obtain posterior inference of model parameters. Then, the Monte Carlo-based expectation maximisation algorithm is used to estimate the model parameters, and the entropy-based overall desirability function is taken as an optimisation objective to obtain the optimal settings. The effectiveness of the proposed method is demonstrated by an additive manufacturing process and a simulation study. Compared with other existing methods, the proposed method can resist the disturbance of outliers, and thus obtain more accurate optimisation results.