In complex physical process characterization, such as the measurement of the regression rate for solid hybrid rocket fuels, where both the observation data and the model used have uncertainties originating from multiple sources, combining these in a systematic way for quantities of interest (QoI) remains a challenge. In this paper, we present a forward propagation uncertainty quantification (UQ) process to produce a probabilistic distribution for the observed regression rate r. We characterized two input data uncertainty sources from the experiment (the distortion from the camera U_c and the non-zero-angle fuel placement U_Y), the prediction and model form uncertainty from the deep neural network (U_m), as well as the variability from the manually segmented images used for training it (U_s). We conducted seven case studies on combinations of these uncertainty sources with the model form uncertainty. The main contribution of this paper is the investigation and inclusion of the experimental image data uncertainties involved, and how to include them in a workflow when the QoI is the result of multiple sequential processes.

中文翻译：

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结合数据和深度学习模型的不确定性：固体燃料回归率测量的应用

在复杂的物理过程表征中，例如固体混合火箭燃料回归率的测量，其中使用的观测数据和模型都具有来自多个来源的不确定性，以系统的方式将它们结合起来以获得感兴趣的数量 (QoI)一个挑战。在本文中，我们提出了前向传播不确定性量化 (UQ) 过程，以生成观察到的回归率 r 的概率分布。我们表征了来自实验的两个输入数据不确定性来源（来自相机的失真U _c和非零角度燃料放置U _Y），来自深度神经网络的预测和模型形式的不确定性（U _m)，以及用于训练它的手动分割图像的可变性 ( U _s )。我们对这些不确定性来源与模型形式不确定性的组合进行了七个案例研究。本文的主要贡献是调查和包含所涉及的实验图像数据不确定性，以及当 QoI 是多个顺序过程的结果时如何将它们包含在工作流中。