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 8 fidelity simulator, x is a design or pro- cess parameter vector, θ is the calibra- tion parameter of low-fidelity analysis, and ∈ is the measurement error. Func- tions η( x , θ) and δ ( x ) are GPs represent- ing the low-fidelity model and model discrepancy, respectively. When only one source of data is available (either from experiments or simulations), then it is modeled as a single GP with y ( x ) = η ( x ). The parameters of these GPs are evaluated through full-Bayesian treat- ment using a Markov Chain Monte Car- lo [11] sampling approach. In the current application, a single data source imple- mentation of GEBHMwas used to create GP models of the quantities of interest. More details on GEBHM can be found in the literature [12,13] . While GEBHM can provide a com- putationally inexpensive probabilistic meta-model to carry out optimization, the uncertainty around the optimized solution can be high if the models are built on small datasets. To identify op- timal solutions with higher confidence in a small number of experimental tri- als, we developed intelligent design and analysis of computer experiments (GE-IDACE) [14] , which provides guidance when seeking new parameters or de- sign settings at which an optimal so- lution can be achieved, while simul- taneously reducing the uncertainty. In GE-IDACE, instead of finding the opti- mum, a new parameter set is sought, which can lead to an improvement over the current best in the dataset. Considering that minimizing is the ob- jective, the improvement is given as I ( x ) = max{ y min - y ( x ),0}, where y min is the current best in the dataset. Because y ( x ) is modeled using GP, there is a predic- tive uncertainty over y , represented by a distribution p y ( x ), which implies that I ( x ) is also a random variable. Under such circumstances, GE-IDACE seeks a location where the expected improve- ment ( EI ) is maximized, where EI is giv- en as: Additional builds and analysis on parameter sets corresponding to the maximum EI are carried out. The under- lying GEBHM model is rebuilt in an iter- ative manner until convergence in the EI is achieved or the experimental bud- get is reached (Fig. 2). EXPERIMENTAL APPROACH: LPBFAM SPECIMEN DESIGN AND CHARACTERIZATION Recognizing the need for high quality data inputs to GEBHM and GE- IDACE, innovative LPBFAM build de- signs coupledwith an automated image analysis routine for quantifying LPB- FAM-specific defects were developed (Fig. 3) [15] . These methods enable rap- id assessment of parameter sensitivi- ty and more reliable, high-throughput data for machine-learning protocols. Gas-atomized, pre-alloyed pow- ders were used to build an array of 0.5 in. diameter cylindrical specimens in an LPBFAM machine, where each speci- men was processed using a different set of LPBFAM conditions. Process parame- ters were varied at every 0.25 in. build- height increment along the cylinder axis to a cylinder height of 1 to 1.5 in. (Fig. 3a). Samples were then cross sectioned in the longitudinal plane, mounted, and polished to a final 0.05 µm finish. Optical micrograph montages capturing the entire speci- men cross section were automatically segmented and filtered to quantify and classify defects resulting from process parameter combinations within each specimen (Fig. 3b). Through the collection of com- position and process parameter-sen- sitive defect data, the framework pro- duces response surfaces as a depic- tion of LPBFAM compatibility, rather than single-point parameter solutions (Fig. 3c). The experimentally derived response surfaces are highly valu- able, especially when considering the multi-objective nature of alloy selection and parameter optimization, as well as the growing need for rapid parame- ter translation across machine platforms and for new compo- nent applications. DATA STORAGE AND MODEL EXECUTION PLATFORM ML models and optimiza- tion protocols mentioned pre- viously are executed within an internal software platform tai- lored for use by additive ma- terials experts. Hosted on commodity computing infra- structure, this platform is de- signed to be applicable to multiple additive modalities and addresses broad data man- agement aspects spanning the entire AM lifecycle [16] . Fig. 2 — GE’s intelligent design and analysis of computer experiments (GE-IDACE).