Bayesian Optimization–based Experimental Design with Multi-output Gaussian Process Regression to Obtain Specific Powder Particle Size Distributions

This paper proposes a Bayesian optimization–based method for optimizing operating parameters in powder processing to achieve desired particle size distributions with a few experimental trials. Such optimization has become increasingly important in recent years due to the trend toward strict quality requirements. A difficulty in applying Bayesian optimization to this task is that the objective variables (i.e., the particle size distributions) are probability distributions, which are required to satisfy the normalization condition. We overcome this difficulty by predicting percentiles using multi-output Gaussian process surrogate models. Experiments on actual equipment showed that the proposed method can provide sufficiently optimized parameter values without either expert knowledge or detailed process modeling. In addition, this paper examines the potential of grey-box modeling for overcoming the limitations of our machine learning approach in extrapolation.