A. Malmberg, K. Chandra, A. Peterson, J. Mead
University of Massachusetts Lowell,
Keywords: additive manufacturing, Bayesian networks, graphical models, predictive modeling, fused filament fabrication
Summary:The design and application of probabilistic graphical models for visualizing and predicting relationships between various types of data derived in additive manufacturing environments is investigated. Of particular interest is the design of a modeling framework that allows the integration of physical models, expert knowledge and experimental data to capture both the invariants and uncertainties in additive manufacturing. The data considered in this work is derived from fused filament fabrication printing from three different commercially available printers. The datasets are available on the NIST materials data repository  and includes processing parameters such as extrusion temperature, layer thickness, print bed temperature and print speed. The mechanical properties of products derived under various combinations of the aforementioned manufacturing parameters are represented by the elastic modulus, the tensile strength at failure, strain to failure and the tear energy. Braconnier, Jensen and Peterson  present a description of the experiments and measurement analysis of the 108 samples produced. A principal component analysis considering a subset of the material and processing features showed various levels of dependence and orthogonal properties among the feature set. However there were also significant differences in these results based on the printer type. This study extends this analysis by examining the likelihood of a particular printer producing a mechanical property in a desired interval of interest and the effect of processing conditions on this metric. The continuous valued mechanical properties are mapped to a discrete set of three levels representing high, medium and low values. The influence of two levels (high, low) of processing parameters is analyzed. Using Bayesian networks (BNs) with processing parameters as the parent nodes, the conditional probabilities of the various material properties are derived. As an example, a query of the probability of achieving a high level of tensile strength conditioned on layer thickness alone, resulted in an increase from 39 to 53 % as layer thickness changed from high to low. When extrusion temperature was added as a dependent variable, this probability increased to 66% for the combination of low layer-thickness and high extrusion-temperature. These results while confirming some of the qualitative observations made in several experimental studies also allows a quantitative comparison of data generated in these experiments. The BN model allows not only a quantification of the effects of processing parameters on material properties, it also enables expected dependencies between mechanical properties as defined by physical models to be explicitly represented.