October AMP_Digital

A D V A N C E D M A T E R I A L S & P R O C E S S E S | O C T O B E R 2 0 1 9 1 7 as gaussian processes (GPs) [8] , poly- nomial chaos expansions [9] , and oth- ers are typically used to build models on sparse, noisy data, predicting both the mean and uncertainty of the out- puts (such as part build quality) as a function of inputs (such as pro- cess parameters). In that spirit, GE Research devel- oped the GE Bayesian hybrid model- ing (GEBHM) framework for advanced Bayesian machine learning with ca- pabilities such as probabilistic meta- modeling, uncertainty propagation and quantification, sensitivity analysis, full Bayesian model calibration, multi- fidelity analysis, and adaptive design of numerical experiments (Fig. 1). The GEBHM framework is based on the ap- proach of Kennedy and O’Hagan [10] to model and fuse simulation and ex- perimental data using GPs. In GEBHM, the high-fidelity model is represent- ed as a linear combination of a low-fi- delity model and a model-discrepancy function: L aser powder bed fusion additive manufacturing (LPBFAM) for struc- tural components requires a rig- orous assessment of the process- ing-structure-property relationships for each material before considering their introduction to service. The high di- mensionality of the process and param- eter space leads not only to increased process development costs, but also raises a significant barrier to discov- ery and insertion of new materials in the AM market. Methods used to devel- op optimum parameters vary consider- ably, from weld-parameter parametric approaches [1] to geometric-based ap- proaches [2,3] and toward the use of melt- pool signatures [4,5] . To reduce the LPBFAM parameter development (PD) cycle time and to en- able the discovery of new alloys better suited for AM, a novel framework incor- porating innovative experimental and model-based approaches was devel- oped. The framework uses probabilistic machine learning (ML), intelligent sam- pling, and optimization protocols, cou- pled with high-throughput printing and characterization to dramatically accel- erate the LBPFAM PD process for new alloys. This article describes the first phase of the probabilisticML framework that was successfully demonstrated to rapidly define optimum parameter sets for commercial high-temperature nick- el superalloys, as well as to guide alloy design and selection for compatibility with LPBFAM. BAYESIAN HYBRID MODELING Meta-modeling or surrogate-mod- eling approaches are commonly used in engineering design communities [6] to explore optimization and design space, among others, when physics-based modeling approaches are not avail- able or are computationally expensive. Some well-known approaches include response surface modeling, support vector machines, artificial neural net- works, and radial basis functions [7] . Most of thesemethods require large vol- umes of data to build an accurate mod- el of the system or process of interest. However, in many engineering prob- lems such as AM, data is sparse and ex- pensive to generate. Additionally, there are significant challenges due to noise in the data. In such scenarios, probabi- listic machine-learning methods such Fig. 1 — GE Bayesian hybridmodeling (GEBHM) framework for advanced probabilistic machine learning. where y denotes the outputs from ei- ther a physical observation or a high-