A methodology enabling the representation, sampling, and identification of spatially-dependent stochastic material parameters on complex structures produced by additive manufacturing is presented. The modeling component builds upon earlier works by the authors and relies on the combination of two ingredients. First, a fractional stochastic partial differential equation is introduced and parameterized in order to automatically capture the complex features of additively manufactured parts. Information-theoretic transport maps are subsequently introduced with the aim of ensuring well-posedness in the forward propagation problem. The identification of stochastic elasticity tensors on titanium scaffolds produced by laser powder bed fusion is then discussed. To this end, we consider an isotropic approximation at a mesoscale where fluctuations are aggregated over several layers, and address both the calibration and validation of the probabilistic model by using different sets of physical structural experiments. Despite the high sensitivity of the forward map to applied boundary conditions, geometrical parameters, and structural porosity, it is shown that the calibrated stochastic model can generate non-vanishing probability levels for all experimental observations.

提出了一种方法，能够对增材制造生产的复杂结构上的空间相关随机材料参数进行表示、采样和识别。建模组件建立在作者早期的工作之上，并依赖于两种成分的组合。首先，引入分数随机偏微分方程并对其进行参数化，以自动捕获增材制造零件的复杂特征。随后引入了信息论传输图，目的是确保前向传播问题中的适定性。激光粉末床融合钛支架随机弹性张量的识别然后进行讨论。为此，我们考虑了中尺度上的各向同性近似，其中波动在几层上聚合，并通过使用不同的物理结构实验集来解决概率模型的校准和验证问题。尽管前向图对应用的边界条件、几何参数和结构孔隙度具有很高的敏感性，但表明校准的随机模型可以为所有实验观测生成非消失的概率水平。