Robust multi-response surface optimisation based on Bayesian quantile model
针对实验数据含异常值导致响应曲面模型不准的问题，提出基于贝叶斯分位数回归的稳健多响应曲面建模与优化方法，通过蒙特卡洛期望最大化算法估计参数，以熵为基础的综合期望函数优化，在增材制造案例中验证了抗异常干扰、结果更准确的效果。
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.