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  1. Bayesian inference allows the transparent communication and systematic updating of model uncertainty as new data become available. When applied to material flow analysis (MFA), however, Bayesian inference is undermined by the difficulty of defining proper priors for the MFA parameters and quantifying the noise in the collected data. We start to address these issues by first deriving and implementing an expert elicitation procedure suitable for generating MFA parameter priors. Second, we propose to learn the data noise concurrent with the parametric uncertainty. These methods are demonstrated using a case study on the 2012 US steel flow. Eight experts are interviewed to elicit distributions on steel flow uncertainty from raw materials to intermediate goods. The experts’ distributions are combined and weighted according to the expertise demonstrated in response to seeding questions. These aggregated distributions form our model parameters’ informative priors. Sensible, weakly informative priors are adopted for learning the data noise. Bayesian inference is then performed to update the parametric and data noise uncertainty given MFA data collected from the United States Geological Survey and the World Steel Association. The results show a reduction in MFA parametric uncertainty when incorporating the collected data. Only a modest reduction in data noise uncertainty was observed using 2012 data; however, greater reductions were achieved when using data from multiple years in the inference. These methods generate transparent MFA and data noise uncertainties learned from data rather than pre-assumed data noise levels, providing a more robust basis for decision-making that affects the system. 
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  2. Informed decision-making for sustainable manufacturing requires accurate manufacturing process environmental impact models with uncertainty quantification (UQ). For emerging manufacturing technologies, there is often insufficient process data available to derive accurate data-driven models. This paper explores an alternative mechanistic modeling approach using easy-to-access data from a given machine to perform Bayesian inference and reduce the uncertainty of model parameters. First, we derive mechanistic models of the cumulative energy demand (CED) for making aluminum (AlSi10) and nylon (PA12) parts using laser powder bed fusion (L-PBF). Initial parametric uncertainty is assigned to the model inputs informed by literature reviews and interviews with industry experts. Second, we identify the most critical sources of uncertainty using variance-based global sensitivity analyses; therefore, reducing the dimension of the problem. For metal and polymer L-PBF, critical uncertainty is related to the adiabatic efficiency of the process (a measure of the efficiency with which the laser energy is used to fuse the powder) and the recoating time per layer between laser scans. Data pertinent to both of these parameters include the part geometry (height and volume) and total build time. Between three and eight data points on part geometry and build time were collected on two different L-PBF machines and Bayesian inference was performed to reduce the uncertainty of the adiabatic efficiency and recoating time per layer on each machine. This approach was validated by subsequently taking direct parameter measurements on these machines during operation. The delivered electricity uncertainty is reduced by 40-70% after performing inference, highlighting the potential to construct accurate energy and environmental impact models of manufacturing processes using small easy-to-access datasets without interfering with the operations of the manufacturing facility. 
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