The present paper aims at applying uncertainty quantification methodologies to process simulations of powder bed fusion of metal. In particular, for a part-scale thermomechanical model of an Inconel 625 super-alloy beam, we study the uncertainties of three process parameters, namely the activation temperature, the powder convection coefficient and the gas convection coefficient. First, we perform a variance-based global sensitivity analysis to study how each uncertain parameter contributes to the variability of the beam displacements. The results allow us to conclude that the gas convection coefficient has little impact and can therefore be fixed to a constant value for subsequent studies. Then, we conduct an inverse uncertainty quantification analysis, based on a Bayesian approach on synthetic displacements data, to quantify the uncertainties of the two remaining parameters, namely the activation temperature and the powder convection coefficient. Finally, we use the results of the inverse uncertainty quantification analysis to perform a data-informed forward uncertainty quantification analysis of the residual strains. Crucially, we make use of surrogate models based on sparse grids to keep to a minimum the computational burden of every step of the uncertainty quantification analysis. The proposed uncertainty quantification workflow allows us to substantially ease the typical trial-and-error approach used to calibrate power bed fusion part-scale models, and to greatly reduce uncertainties on the numerical prediction of the residual strains. In particular, we demonstrate the possibility of using displacement measurements to obtain a data-informed probability density function of the residual strains, a quantity much more complex to measure than displacements.

翻译：本文旨在将不确定性量化方法应用于金属粉末床熔融工艺仿真。针对Inconel 625镍基高温合金梁的部件级热力学模型，我们研究了三个工艺参数的不确定性，即激活温度、粉末对流系数和气体对流系数。首先，我们开展基于方差的全局敏感性分析，以探究各不确定参数对梁位移变异性的贡献。结果表明气体对流系数影响甚微，故可在后续研究中将其固定为常数值。随后，基于贝叶斯方法对合成位移数据进行逆向不确定性量化分析，以量化剩余两个参数（激活温度与粉末对流系数）的不确定性。最后，利用逆向不确定性量化分析结果，开展基于数据的残余应变前向不确定性量化分析。关键之处在于，我们采用基于稀疏网格的代理模型，以最大程度降低不确定性量化分析各步骤的计算负担。所提出的不确定性量化工作流程能显著简化校准粉末床熔融部件级模型时常用的试错法，并大幅降低残余应变数值预测的不确定性。具体而言，我们证明了利用位移测量值获取基于数据的残余应变概率密度函数的可行性——该物理量的测量复杂度远高于位移。