Combined Data and Deep Learning Model Uncertainties: An Application to the Measurement of Solid Fuel Regression Rate

TL;DR

This paper develops a systematic uncertainty quantification workflow for measuring solid fuel regression rates, integrating experimental data uncertainties and deep learning model uncertainties to produce probabilistic estimates.

Contribution

It introduces a novel approach to incorporate experimental image data uncertainties into a deep learning-based measurement process for physical quantities.

Findings

Uncertainty propagation produces probabilistic regression rate estimates.

Experimental data uncertainties significantly affect the measurement accuracy.

The workflow effectively combines multiple uncertainty sources in complex physical process modeling.

Abstract

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 $\dot{r}$. We characterized two input data uncertainty sources from the experiment (the distortion from the camera $U_c$ and the non-zero angle fuel placement $U_\gamma$), 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.