Joint Parameter and State-Space Modelling of Manufacturing Processes using Gaussian Processes

Manufacturing process optimization is an open question, where Bayesian decision theoretic methods have shown considerable promise. One such is Bayesian optimization, with Gaussian Process (GP) surrogate model. This paper explores Gaussian Processes networks to jointly use parameter and observed state to predict the output(s) of a manufacturing process. The Gaussian process network that represents the paths from parameters to state-space to tasks, provides a methodology to ‘look inside’ the black-box of complex manufacturing processes. We present a comparative analysis of this method against the multi-task Gaussian processes and single-task counterparts, highlighting the benefits and drawbacks of each in modelling the behavior of such processes. We show the benefits of the proposed approach using numerical experiments. We show that we are able to improve the output prediction by additional sensor observations from inside the process at training time without needing those sensor observations for predicting product quality given the process parameters.