Applying Bayesian Statistical Methods to Optimise Processes Within Additive Manufacturing

Additive Manufacturing (AM), otherwise known as 3D printing, is the process of building 3D objects based on some 3D model, typically provided by some computer-aided design. AM comprises multiple methodologies which can fabricate 3D objects with several different materials. While AM has been a fast-developing field for several years, there are notable gaps in the research for applications of statistically sound methods that are able to answer a wide variety of important and complex questions. Due to savings on cost and time, these methods can be highly beneficial. This works provides a robust process for estimating relationships between multiple output variables and input variables simultaneously with a 'forward' model, which accounts for measurement error in the data and incorporates expert opinion into the modelling. This expert opinion, alongside the available data, provides a more complete understanding of the relationship to be estimated. The ultimate aim of this work is the optimisation of the input variables in order to produce desired values for multiple output variables. With the use of Bayesian statistics, these methods provide an intuitive process for this optimisation by inverting the fitted relationship identified in the forward modelling. Two modelling methods are demonstrated: errors-in-variables Bayesian regression, and errors-in-variables Gaussian processes. The former is a 'parametric' method, which estimates model parameters based on a fixed, predetermined relationship. The latter is a 'nonparametric' method, which does not assume such a relationship, instead assuming a multivariate normal distribution for the output variables, whose covariance is informed by spatial correlation between the input variables. The modelling process for these statistical methods is developed with simulated data, followed by an application to a real-data example, looking at optimisation of powder properties to provide ideal powder flow and powder bed deposition for improving laser sintering.